The Annals of probability, ISSN 0091-1798, 2013, Volume 41, Issue 5, pp. 3284 - 3305

We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was...

Embeddings | Covariance | Center of gravity | Separable spaces | Hilbert spaces | Fourier transformations | Euclidean space | Mathematical moments | Random variables | Hypothesis testing | Distance correlation | Brownian covariance | Negative type | Independence | POSITIVE-DEFINITE FUNCTIONS | hypothesis testing | STATISTICS & PROBABILITY | independence | distance correlation | 62H15 | 30L05 | 62G20 | 62H20 | 51K99

Embeddings | Covariance | Center of gravity | Separable spaces | Hilbert spaces | Fourier transformations | Euclidean space | Mathematical moments | Random variables | Hypothesis testing | Distance correlation | Brownian covariance | Negative type | Independence | POSITIVE-DEFINITE FUNCTIONS | hypothesis testing | STATISTICS & PROBABILITY | independence | distance correlation | 62H15 | 30L05 | 62G20 | 62H20 | 51K99

Journal Article

Advances in applied probability, ISSN 0001-8678, 07/2016, Volume 48, Issue A, pp. 145 - 152

.... One significant aspect of the theory is directed at identifying the level of generality of the product probability space that accommodates the event under study...

PROBABILITY | separable space | measure-space isomorphism | Influence | STATISTICS & PROBABILITY | VARIABLES | sharp threshold | product space | Probability | Statistical analysis | Combinatorial analysis

PROBABILITY | separable space | measure-space isomorphism | Influence | STATISTICS & PROBABILITY | VARIABLES | sharp threshold | product space | Probability | Statistical analysis | Combinatorial analysis

Journal Article

The Journal of symbolic logic, ISSN 0022-4812, 12/2013, Volume 78, Issue 4, pp. 1055 - 1085

We say that an uncountable metric space is computably categorical if every two computable structures on this space are equivalent up to a computable isometry...

Categoricity | Algebra | Computer analysis | Separable spaces | Hilbert spaces | Mathematical logic | Banach space | Automorphisms | Completely Hausdorff spaces | Computability | Metric space theory | Computable analysis | MATHEMATICS | metric space theory | LINEAR-ORDERINGS | LOGIC | Theorems (Mathematics) | Metric spaces | Banach spaces | Analysis | Tests, problems and exercises

Categoricity | Algebra | Computer analysis | Separable spaces | Hilbert spaces | Mathematical logic | Banach space | Automorphisms | Completely Hausdorff spaces | Computability | Metric space theory | Computable analysis | MATHEMATICS | metric space theory | LINEAR-ORDERINGS | LOGIC | Theorems (Mathematics) | Metric spaces | Banach spaces | Analysis | Tests, problems and exercises

Journal Article

The Annals of probability, ISSN 0091-1798, 2007, Volume 35, Issue 4, pp. 1438 - 1478

...)$, where H is a separable Hilbert space and E is a UMD Banach space (i.e., a space in which martingale differences are unconditional...

Brownian motion | Measurability | Separable spaces | Hilbert spaces | Random variables | Banach space | Stopping distances | Martingales | Probabilities | Burkholder-davis-gundy inequalities | γ-radonifying operators | Martingale representation theorem | UMD banach spaces | Stochastic integration in banach spaces | Cylindrical brownian motion | Decoupling inequalities | MARTINGALES | cylindrical Brownian motion | stochastic integration in Banach spaces | UMD Banach spaces | decoupling inequalities | STATISTICS & PROBABILITY | VALUES | martingale representation theorem | gamma-radonifying operators | Burkholder-Davis-Gundy inequalities | 28C20 | Stochastic integration in Banach spaces | 60B11 | 60H05 | Burkholder–Davis–Gundy inequalities

Brownian motion | Measurability | Separable spaces | Hilbert spaces | Random variables | Banach space | Stopping distances | Martingales | Probabilities | Burkholder-davis-gundy inequalities | γ-radonifying operators | Martingale representation theorem | UMD banach spaces | Stochastic integration in banach spaces | Cylindrical brownian motion | Decoupling inequalities | MARTINGALES | cylindrical Brownian motion | stochastic integration in Banach spaces | UMD Banach spaces | decoupling inequalities | STATISTICS & PROBABILITY | VALUES | martingale representation theorem | gamma-radonifying operators | Burkholder-Davis-Gundy inequalities | 28C20 | Stochastic integration in Banach spaces | 60B11 | 60H05 | Burkholder–Davis–Gundy inequalities

Journal Article

New Journal of Physics, ISSN 1367-2630, 04/2015, Volume 17, Issue 4, pp. 1 - 13

.... Searching the high-dimensional quantum state space for a global maximum of an objective function with many local maxima or evaluating an integral over a region in the quantum state space are but two...

MCMC | Quantum state space | Monte Carlo | Sampling | Independence sampling | independence sampling | DISTRIBUTIONS | SET | PHYSICS, MULTIDISCIPLINARY | quantum state space | sampling | VOLUME | SEPARABLE STATES | Monte Carlo method | Statistical analysis | Computer simulation | Markov chains | Statistical methods | Qubits (quantum computing) | Markov analysis | Maxima | Quantum phenomena | Operators (mathematics) | Quantum computing | Mathematical analysis | Entangled states | Importance sampling | Physics - Quantum Physics

MCMC | Quantum state space | Monte Carlo | Sampling | Independence sampling | independence sampling | DISTRIBUTIONS | SET | PHYSICS, MULTIDISCIPLINARY | quantum state space | sampling | VOLUME | SEPARABLE STATES | Monte Carlo method | Statistical analysis | Computer simulation | Markov chains | Statistical methods | Qubits (quantum computing) | Markov analysis | Maxima | Quantum phenomena | Operators (mathematics) | Quantum computing | Mathematical analysis | Entangled states | Importance sampling | Physics - Quantum Physics

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2016, Volume 368, Issue 4, pp. 2865 - 2889

Solving a problem of F. Jordan, we show that for every unbounded tower set X\subseteq \mathbb{R}, the space \operatorname {C}_\mathrm {p}(X) is productively...

C-P(X) | Gerlits-Nagy property () | Sierpinski set | selectively separable | countable fan tightness | GAMES | Gerlits-Nagy property gamma | Menger property | special sets of real numbers | MATHEMATICS | Hurewicz property | Rothberger property | Cohen forcing | SEPARABILITY | selection principles | C-p theory | REAL NUMBERS | COMBINATORICS | MEASURE ZERO SETS

C-P(X) | Gerlits-Nagy property () | Sierpinski set | selectively separable | countable fan tightness | GAMES | Gerlits-Nagy property gamma | Menger property | special sets of real numbers | MATHEMATICS | Hurewicz property | Rothberger property | Cohen forcing | SEPARABILITY | selection principles | C-p theory | REAL NUMBERS | COMBINATORICS | MEASURE ZERO SETS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2016, Volume 270, Issue 4, pp. 1361 - 1378

Asplund property of a Banach space X is characterized by the existence of a rich family, in the product X×X...

Rich family | Fréchet subdifferential | Asplund space | Separable reduction | MATHEMATICS | Frechet subdifferential

Rich family | Fréchet subdifferential | Asplund space | Separable reduction | MATHEMATICS | Frechet subdifferential

Journal Article

Topology and its Applications, ISSN 0166-8641, 04/2017, Volume 221, pp. 465 - 475

We show that if Y is a dense subspace of a Tychonoff space X, then w(X)≤nw(Y)Nag(Y), where Nag(Y) is the Nagami number of Y...

Separable | Lindelöf Σ-space | Countably compact | Density | Weight | ω-Narrow | MATHEMATICS | MATHEMATICS, APPLIED | Lindelof Sigma-space | ALEXANDROFF | omega-Narrow

Separable | Lindelöf Σ-space | Countably compact | Density | Weight | ω-Narrow | MATHEMATICS | MATHEMATICS, APPLIED | Lindelof Sigma-space | ALEXANDROFF | omega-Narrow

Journal Article

Topology and its Applications, ISSN 0166-8641, 2009, Volume 156, Issue 7, pp. 1241 - 1252

A space X is selectively separable if for every sequence ( D n : n ∈ ω ) of dense subspaces of X one can select finite F n ⊂ D n so that ⋃ { F n : n ∈ ω } is dense in X...

Hurewicz space | Selection principles | Separable space | R-separable space | Menger space | Gerlitz–Nagy property [formula omitted] | [formula omitted] space | M-separable space | GN-separable space | Rothberger space | H-separable space | space | Gerlitz-Nagy property () | FUNCTION-SPACES | MATHEMATICS, APPLIED | PROPERTY | COVERS | MATHEMATICS | CATEGORY | C-p space | SETS

Hurewicz space | Selection principles | Separable space | R-separable space | Menger space | Gerlitz–Nagy property [formula omitted] | [formula omitted] space | M-separable space | GN-separable space | Rothberger space | H-separable space | space | Gerlitz-Nagy property () | FUNCTION-SPACES | MATHEMATICS, APPLIED | PROPERTY | COVERS | MATHEMATICS | CATEGORY | C-p space | SETS

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 9/2016, Volume 181, Issue 1, pp. 169 - 176

...) for separable Banach spaces. We show that a closed subspace of the Gurariy space that is an almost isometric ideal is itself the Gurariy space...

Secondary 46E40 | Extension of isometries | Almost isometric ideals | Gurariy space | Primary 46B20 | Separable spaces | Mathematics, general | Mathematics | L^1$$ L 1 -predual spaces | predual spaces | MATHEMATICS | L-1-predual spaces

Secondary 46E40 | Extension of isometries | Almost isometric ideals | Gurariy space | Primary 46B20 | Separable spaces | Mathematics, general | Mathematics | L^1$$ L 1 -predual spaces | predual spaces | MATHEMATICS | L-1-predual spaces

Journal Article

The Annals of probability, ISSN 0091-1798, 9/2012, Volume 40, Issue 5, pp. 2264 - 2297

We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space...

Brownian motion | Determinism | Approximation | Mathematical theorems | Differential equations | Uniqueness | Separable spaces | Mathematics | Martingales | Probabilities | Filtration | Separable | Grönwall inequality | General | Comparison theorem | Bsde | Nonlinear expectation | Probability space | CONSISTENT | nonlinear expectation | STOCHASTIC DIFFERENTIAL-EQUATIONS | general filtration | separable probability space | STATISTICS & PROBABILITY | Gronwall inequality | BSDE | comparison theorem | 60H10 | 60H20 | 91B16

Brownian motion | Determinism | Approximation | Mathematical theorems | Differential equations | Uniqueness | Separable spaces | Mathematics | Martingales | Probabilities | Filtration | Separable | Grönwall inequality | General | Comparison theorem | Bsde | Nonlinear expectation | Probability space | CONSISTENT | nonlinear expectation | STOCHASTIC DIFFERENTIAL-EQUATIONS | general filtration | separable probability space | STATISTICS & PROBABILITY | Gronwall inequality | BSDE | comparison theorem | 60H10 | 60H20 | 91B16

Journal Article

Filomat, ISSN 0354-5180, 2018, Volume 32, Issue 15, pp. 5403 - 5413

For a Tychonoff space X, we denote by C-k(X) the space of all real-valued continuous functions on X with the compact-open topology...

Compact-open topology | Strongly sequentially separable | M-separable | Selection principles | Sequentially separable | set | Function space | Selectively sequentially separable | R-separable | MATHEMATICS, APPLIED | PROPERTY | COVERS | function space | Compact open topology | selectively sequentially separable | MATHEMATICS | gamma(k)-set | SETS | sequentially separable | strongly sequentially separable | selection principles

Compact-open topology | Strongly sequentially separable | M-separable | Selection principles | Sequentially separable | set | Function space | Selectively sequentially separable | R-separable | MATHEMATICS, APPLIED | PROPERTY | COVERS | function space | Compact open topology | selectively sequentially separable | MATHEMATICS | gamma(k)-set | SETS | sequentially separable | strongly sequentially separable | selection principles

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 10/2016, Volume 66, Issue 5, pp. 1119 - 1138

We focus on measurability and integrability for set valued functions in non-necessarily separable Fréchet spaces...

Primary 28B20 | Secondary 28C05 | measurable multifunction | non-separable Fréchet space | 54E35 | 34A60 | integrable multifunction | Volterra inclusion | LOCALLY CONVEX-SPACES | MEASURABILITY | MULTIFUNCTIONS | THEOREM | DECOMPOSITION | MULTIVALUED FUNCTIONS | MATHEMATICS | BANACH-SPACES | non-separable Frechet space | SELECTIONS | ORDINARY DIFFERENTIAL-EQUATIONS | CLOSED SUBSETS | Functions | Research | Vector spaces | Functional equations | Mathematical research

Primary 28B20 | Secondary 28C05 | measurable multifunction | non-separable Fréchet space | 54E35 | 34A60 | integrable multifunction | Volterra inclusion | LOCALLY CONVEX-SPACES | MEASURABILITY | MULTIFUNCTIONS | THEOREM | DECOMPOSITION | MULTIVALUED FUNCTIONS | MATHEMATICS | BANACH-SPACES | non-separable Frechet space | SELECTIONS | ORDINARY DIFFERENTIAL-EQUATIONS | CLOSED SUBSETS | Functions | Research | Vector spaces | Functional equations | Mathematical research

Journal Article

14.
Full Text
THE SPATIAL DISTRIBUTION IN INFINITE DIMENSIONAL SPACES AND RELATED QUANTILES AND DEPTHS

The Annals of statistics, ISSN 0090-5364, 6/2014, Volume 42, Issue 3, pp. 1203 - 1231

.... In this paper, we investigate the concept of spatial distribution for data in infinite dimensional Banach spaces...

Brownian motion | Statistical median | Datasets | Spatial distribution | Probability distributions | Covariance | Separable spaces | Hilbert spaces | Mathematical functions | Banach space | Karhunen-Loève expansion | DD-plot | Gâteaux derivative | Smooth Banach space | Asymptotic relative efficiency | Donsker property | Glivenko-Cantelli property | Bahadur representation | TESTS | Karhunen-Loeve expansion | STATISTICS & PROBABILITY | smooth Banach space | FUNCTIONAL DATA | Gateaux derivative | NOTION | Statistics - Methodology | 62G05 | 60G12 | Glivenko–Cantelli property | 60B12 | Karhunen–Loève expansion

Brownian motion | Statistical median | Datasets | Spatial distribution | Probability distributions | Covariance | Separable spaces | Hilbert spaces | Mathematical functions | Banach space | Karhunen-Loève expansion | DD-plot | Gâteaux derivative | Smooth Banach space | Asymptotic relative efficiency | Donsker property | Glivenko-Cantelli property | Bahadur representation | TESTS | Karhunen-Loeve expansion | STATISTICS & PROBABILITY | smooth Banach space | FUNCTIONAL DATA | Gateaux derivative | NOTION | Statistics - Methodology | 62G05 | 60G12 | Glivenko–Cantelli property | 60B12 | Karhunen–Loève expansion

Journal Article

New York Journal of Mathematics, ISSN 1076-9803, 2016, Volume 22, pp. 605 - 613

We present: i) an example of a Banach space of universal disposition that is not separably injective; ii...

Separable complementation property | Separable injective | Banach spaces of universal disposition | MATHEMATICS | separable injective | EXTENSION | separable complementation property | C(K)-SPACES

Separable complementation property | Separable injective | Banach spaces of universal disposition | MATHEMATICS | separable injective | EXTENSION | separable complementation property | C(K)-SPACES

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 4/2018, Volume 154, Issue 2, pp. 362 - 377

For a Tychonoff space X, we denote by C p (X) the space of all real-valued continuous functions on X with the topology of pointwise convergence...

{S_1(B_{\Omega}, B_{\Gamma})}$$ S 1 ( B Ω , B Γ ) | Baire function | 54C35 | {\mathfrak{b}}$$ b -Sierpiński set | 37F20 | Mathematics | function space | selection principle | C p space | strongly sequentially separable | sequentially separable | {\gamma}$$ γ -set | Mathematics, general | 26A03 | Gerlits–Nagy $${\gamma}$$ γ property | 03E75 | {S_1(\Omega, \Gamma)}$$ S 1 ( Ω , Γ ) | {\sigma}$$ σ -set | OPEN COVERS | b-Sierpinski set | S-1( B-Omega, B-Gamma) | COMPACT SPACES | S1(Omega, Gamma) | DENSITY | MATHEMATICS | sigma-set | gamma-set | Gerlits-Nagy gamma property | C-p space | CONVERGENCE | POINTWISE | COMBINATORICS

{S_1(B_{\Omega}, B_{\Gamma})}$$ S 1 ( B Ω , B Γ ) | Baire function | 54C35 | {\mathfrak{b}}$$ b -Sierpiński set | 37F20 | Mathematics | function space | selection principle | C p space | strongly sequentially separable | sequentially separable | {\gamma}$$ γ -set | Mathematics, general | 26A03 | Gerlits–Nagy $${\gamma}$$ γ property | 03E75 | {S_1(\Omega, \Gamma)}$$ S 1 ( Ω , Γ ) | {\sigma}$$ σ -set | OPEN COVERS | b-Sierpinski set | S-1( B-Omega, B-Gamma) | COMPACT SPACES | S1(Omega, Gamma) | DENSITY | MATHEMATICS | sigma-set | gamma-set | Gerlits-Nagy gamma property | C-p space | CONVERGENCE | POINTWISE | COMBINATORICS

Journal Article

Fundamenta Mathematicae, ISSN 0016-2736, 2012, Volume 217, Issue 3, pp. 189 - 210

We generalize to the non-separable context a theorem of Levi characterizing Baire analytic spaces...

Analytic sets | Automatic continuity | Non-commutative groups | Analytic cantor theorem | Nikodym's stability theorem | Shift-compactness | Group-norm | Analytic Baire theorem | Open mapping | Non-separable descriptive topology | TOPOLOGICAL-GROUPS | group-norm | METRIC-SPACES | non-commutative groups | MATHEMATICS | analytic sets | CONTINUITY | MAPS | automatic continuity | non-separable descriptive topology | IMAGES | shift-compactness | THEOREMS | SETS | analytic Cantor theorem | MAPPINGS | analytic Baire theorem | Nikodym's Stability Theorem | open mapping

Analytic sets | Automatic continuity | Non-commutative groups | Analytic cantor theorem | Nikodym's stability theorem | Shift-compactness | Group-norm | Analytic Baire theorem | Open mapping | Non-separable descriptive topology | TOPOLOGICAL-GROUPS | group-norm | METRIC-SPACES | non-commutative groups | MATHEMATICS | analytic sets | CONTINUITY | MAPS | automatic continuity | non-separable descriptive topology | IMAGES | shift-compactness | THEOREMS | SETS | analytic Cantor theorem | MAPPINGS | analytic Baire theorem | Nikodym's Stability Theorem | open mapping

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2011, Volume 139, Issue 8, pp. 2777 - 2782

.... We analyze what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well...

Separable spaces | Real numbers | Banach space | Quotients | Daugavet property | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES

Separable spaces | Real numbers | Banach space | Quotients | Daugavet property | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 1/2017, Volume 182, Issue 1, pp. 39 - 47

In 1983 P. Domański investigated the question: For which separable topological vector spaces E, does the separable space have a nonseparable closed vector subspace, where $$\hbox {c...

Locally convex topological vector space | Mathematics, general | Mathematics | 46A03 | Separable topological space | 54D65 | MATHEMATICS | DENSITY CHARACTER | Resveratrol

Locally convex topological vector space | Mathematics, general | Mathematics | 46A03 | Separable topological space | 54D65 | MATHEMATICS | DENSITY CHARACTER | Resveratrol

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2010, Volume 362, Issue 9, pp. 4871 - 4900

We introduce the class of slicely countably determined Banach spaces which contains in particular all spaces with the Radon-Nikodym property and all spaces without copies of \ell _1...

Unit ball | Topological theorems | Radon | Separable spaces | Linear transformations | Topology | Banach space | Lurs | Topological spaces | Containing of l | Radon-Nikodým property | Daugavet equation | Numerical index | Numerical radius | Asplund spaces | Narrow operators | MATHEMATICS | numerical index | containing of l | DAUGAVET PROPERTY | narrow operators | SUBSETS | Radon-Nikodym property

Unit ball | Topological theorems | Radon | Separable spaces | Linear transformations | Topology | Banach space | Lurs | Topological spaces | Containing of l | Radon-Nikodým property | Daugavet equation | Numerical index | Numerical radius | Asplund spaces | Narrow operators | MATHEMATICS | numerical index | containing of l | DAUGAVET PROPERTY | narrow operators | SUBSETS | Radon-Nikodym property

Journal Article

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