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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 2, pp. 1267 - 1283
We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop–Phelp's theorem and James' compactness... 
Weakly compact | James' compactness theorem | MATHEMATICS | WEAK COMPACTNESS | MATHEMATICS, APPLIED | BOUNDARIES | CONVEX-SETS
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2018, Volume 25, Issue 4, pp. 1335 - 1344
The following result is proved: Let A be a convex bounded non weakly relatively compact subset of a Banach space E. We fix a convex weakly compact subset D of... 
Weakly compact | James' compactness theorem | MATHEMATICS | weakly compact set | WEAK COMPACTNESS
Journal Article
Annals of Global Analysis and Geometry, ISSN 0232-704X, 12/2018, Volume 54, Issue 4, pp. 541 - 549
Journal Article
Topology and its Applications, ISSN 0166-8641, 02/2019, Volume 252, pp. 158 - 168
This manuscript extends both Cantor intersection theorem and Cantor–Kuratowski intersection theorem from the setting of metric spaces to the setting of... 
Uniformizable space | Admissible space | Measure of noncompactness | Completeness | Compactness | Total boundedness | MATHEMATICS | ATTRACTORS | MATHEMATICS, APPLIED | SEMIGROUP ACTIONS | STABILITY
Journal Article
Expositiones Mathematicae, ISSN 0723-0869, 2010, Volume 28, Issue 4, pp. 385 - 394
We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their... 
Compactness in Lp | Kolmogorov–Riesz compactness theorem | Compactness in L | Kolmogorov-Riesz compactness theorem | MATHEMATICS | Compactness in L-P
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 10/2012, Volume 14, Issue 5, pp. 1250033 - 1250014
Journal Article
Expositiones Mathematicae, ISSN 0723-0869, 03/2019, Volume 37, Issue 1, pp. 84 - 91
The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical... 
Kolmogorov–Riesz compactness theorem | Compactness in [formula omitted] | Compactness in L | MATHEMATICS | Kolmogorov-Riesz compactness theorem | Compactness in L-P | SPACES | Mathematics - Functional Analysis
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2017, Volume 449, Issue 1, pp. 528 - 530
We provide a short proof of the following fact: If X is a Banach space, A and B are bounded, closed and convex sets with dist(A,B)>0 and every x⁎∈X⁎ with the... 
Weakly compact sets | James' theorem | MATHEMATICS | MATHEMATICS, APPLIED | COMPACTNESS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2020, Volume 485, Issue 1, p. 123764
Let A be a closed, convex, bounded and non weakly compact subset of a Banach space E with 0∉A. Let us fix a convex and weakly compact subset W of E, a... 
Reflexivity | Mackey topology | Weak compactness | Non attaining linear functionals | Risk measures | Lebesgue property | MATHEMATICS | MATHEMATICS, APPLIED | SETS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2019, Volume 470, Issue 1, pp. 279 - 291
For a vector measure m, with values in a Banach space, we analyze the localization of uniformly integrable subsets of scalar integrable functions with respect... 
Uniform integrability | Vector measure | Compactness | Orlicz spaces | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | RESPECT
Journal Article
Annals of Applied Probability, ISSN 1050-5164, 06/2018, Volume 28, Issue 3, pp. 1379 - 1422
We study the behavior of second-order degenerate elliptic systems in divergence form with random coefficients which are stationary and ergodic. Assuming moment... 
Degenerate elliptic system | Liouville theorem | Stochastic homogenization | Large-scale regularity | Degenerate elliptic equation | degenerate elliptic system | EQUATIONS | STATISTICS & PROBABILITY | HARMONIC-FUNCTIONS | large-scale regularity | INVARIANCE-PRINCIPLE | stochastic homogenization | COMPACTNESS METHODS
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2019, Volume 58, Issue 4, pp. 1 - 13
We prove several classification results for p-Laplacian problems on bounded and unbounded domains, and deal with qualitative properties of sign-changing... 
35J92 (35B33 · 35B53 · 35B38) | Mathematics | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED | CLASSIFICATION | GLOBAL COMPACTNESS RESULT | REGULARITY
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2016, Volume 437, Issue 2, pp. 870 - 881
We prove an extension to the finitely additive setting of the theorem of Halmos and Savage. From this we deduce extensions of classical results of Drewnowski... 
Yan theorem | Lebesgue decomposition | Halmos–Savage theorem | Weak compactness | Halmos-Savage theorem | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR FUNCTIONALS | Mathematics - Probability
Journal Article
Journal of Intelligent and Fuzzy Systems, ISSN 1064-1246, 2019, Volume 36, Issue 6, pp. 6663 - 6668
In this paper, using the structures of (L, L)-fuzzy product supratopological spaces which were introduced by Hu Zhao and Gui-xiu Chen, we give a proof of... 
Fuzzy compactness | Generalized Tychonoff theorem | Product topological spaces | (L M)-fuzzy supratopology | product topological spaces | fuzzy compactness | COMPACTNESS | generalized Tychonoff theorem | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | (L, M)-fuzzy supratopology | Theorems | Graphical user interface | Fuzzy
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 01/2015, Volume 268, Issue 1, pp. 194 - 209
Let X and Y be Banach spaces and F⊂BY⁎. Endow Y with the topology τF of pointwise convergence on F. Assume that T:X⁎→Y is a bounded linear operator which is... 
James sup theorem | The [formula omitted]-theorem | Boundary | The ℓ1-theorem | MATHEMATICS | WEAK COMPACTNESS | MINIMAX | BOUNDARIES | REFLEXIVITY | BALLS | BANACH-SPACES | The l-theorem | CONVEX-SETS
Journal Article
Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 04/2018, Volume 19, Issue 2, pp. 1 - 49
We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface $\unicode[STIX]{x1D6F4}$. As a corollary we obtain a new... 
differential geometry | compactness theorem | metric geometry | Alexandrov surfaces with bounded integral curvature | conical singularities | Theorems | Singularities | Integrals | Curvature
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2019, Volume 277, Issue 7, pp. 2092 - 2116
Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the... 
Compactness theorem | Mean curvature | Boundary Yamabe problem | Manifolds with boundary | YAMABE PROBLEM | EXISTENCE | PROOF | MATHEMATICS | CONFORMAL DEFORMATION | CURVATURE | BLOW-UP PHENOMENA | MANIFOLDS | EQUATION | UNIQUENESS THEOREMS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2017, Volume 452, Issue 2, pp. 1101 - 1127
Locally L0-convex modules were introduced in Filipovic et al. (2009) [10] as the analytic basis for the study of conditional risk measures. Later, the algebra... 
Conditional convex risk measure | Stability properties | Locally [formula omitted]-convex module | James' compactness theorem | Conditionally locally convex space | Jouini–Schachermayer–Touzi theorem | Locally L | convex module
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2017, Volume 92, Issue 4, pp. 751 - 776
We prove that a sequence of Fueter sections of a bundle of compact hyperkähler manifolds $\mathfrak{X}$ over a 3-manifold $M$ with bounded energy converges... 
Global analysis, analysis on manifolds | Differential geometry | Bubbling | Hyperkähler manifolds | Fueter sections | Compactness | MATHEMATICS | MAPS | bubbling | compactness | hyperkahler manifolds | GEOMETRY | Mathematics - Differential Geometry
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2018, Volume 460, Issue 2, pp. 682 - 702
Let X and Y be Banach spaces and let Ω be a compact Hausdorff space. By the classical Bartle–Dunford–Schwartz theorem, any operator S∈L(C(Ω),Y) admits an... 
Operators on function spaces | Banach spaces | Operator-valued measure | p-Compactness | Integral representation | q-Semivariation | MATHEMATICS | MATHEMATICS, APPLIED | VALUED FUNCTION-SPACES | PRODUCTS | BANACH-SPACES | OPERATORS
Journal Article
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