Open problems in Banach spaces and measure theory
DOI10.2989/16073606.2017.1315749zbMath1426.28026arXiv1607.07787OpenAlexW2963411362MaRDI QIDQ5236112
Publication date: 15 October 2019
Published in: Quaestiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.07787
Pettis integralvector measureMcShane integralBanach spaceRiemann integralBorel \(\sigma\)-algebraLebesgue-Bochner spacemeasurable selectorBaire \(\sigma\)-algebra
Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of vector- and operator-valued functions (46E40) Vector-valued set functions, measures and integrals (28B05) Compactness in Banach (or normed) spaces (46B50) Nonseparable Banach spaces (46B26)
Cites Work
- On coincidence of Pettis and McShane integrability
- Weak Compactness in L 1 (μ, X)
- Weak Baire measurability of the balls in a Banach space
- Compactness in L1of a vector measure
- Remarks on Riemann-integration of vector-valued functions
- Biorthogonal systems in Banach spaces
- Set-valued analysis
- On the equivalence of McShane and Pettis integrability in non-separable Banach spaces
- On various modes of scalar convergence in \(L_0({\mathfrak X})\)
- On the weak property of Lebesgue of \(L^1(\Omega,\Sigma,\mu)\)
- Weak continuity of Riemann integrable functions in Lebesgue-Bochner spaces
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Riemann integrability versus weak continuity
- Convex combinations of weak\(^*\)-convergent sequences and the Mackey topology
- Measurability in \(C(2^\kappa)\) and Kunen cardinals
- On a certain class of \(\mathcal K_{\sigma\delta}\) Banach spaces
- Subspaces of \(L_p\) that embed into \(L_p(\mu)\) with \(\mu\) finite
- Tukey classification of some ideals on \(\omega\) and the lattices of weakly compact sets in Banach spaces
- On some problems concerning Borel structures in function spaces
- The McShane integral in weakly compactly generated spaces
- Boundaries for Banach spaces determine weak compactness
- Integration in Hilbert generated Banach spaces
- Some approximation properties of Banach spaces and Banach lattices
- Lebesgue-Bochner spaces, decomposable sets and strong weakly compact generation
- Series in Banach spaces: conditional and unconditional convergence. Transl. from the Russian by Andrei Iacob
- On Baire measurability in spaces of continuous functions
- Description of the limit set of Henstock-Kurzweil integral sums of vector-valued functions
- Operators into \(L^ 1\) of a vector measure and applications to Banach lattices
- On the SWCG property in Lebesgue-Bochner spaces
- Weakly extremal properties of Banach spaces
- Asymptotic structure of Banach spaces and Riemann integration
- On a problem of H.\,P.\ Rosenthal concerning operators on \(C\)[0,1]
- Measurable selectors and set-valued Pettis integral in non-separable Banach spaces
- On Banach spaces with the Gelfand-Phillips property
- On strongly WCG Banach spaces
- Asplund operators and a.e. convergence
- Séparabilité vague dans l'espace des mesures sur un compact
- Riemann integration in Banach spaces
- A decomposition theorem for additive set-functions with applications to Pettis integrals and ergodic means
- Espaces de Banachs faiblement K-analytiques
- The dual space of \({\mathcal L}^ 1(\mu)\) for a vector measure \(\mu\)
- When \(L^ 1\) of a vector measure is an AL-space
- On the integration of vector-valued functions
- The generalized McShane integral
- Kernels of surjections from \({\mathcal L}_1\)-spaces with an application to Sidon sets
- Banach spaces of vector-valued functions
- Hilbert-generated spaces.
- When do McShane and Pettis integrals coincide?
- On weakly Radon-Nikodým compact spaces
- Cofinal types of topological directed orders.
- Geometric aspects of convex sets with the Radon-Nikodym property
- Some remarks on countably determined measures and uniform distribution of sequences
- Three sequential properties of dual Banach spaces in the weak\(^*\) topology
- On Borel structures in the Banach space \(C({\beta}{\omega})\)
- Multi-applications mesurables à valeurs convexes compactes
- Conditional weak compactness in certain inductive tensor products
- Some results concerning L\(^p(\mu)\)-spaces
- Banach space theory. The basis for linear and nonlinear analysis
- Compactness of the integration operator associated with a vector measure
- Factorization of vector measures and their integration operators
- Representations of dynamical systems on Banach spaces not containing $l_{1}$
- Extension operators on balls and on spaces of finite sets
- Summability in L1 of a vector measure
- Operator ideal properties of vector measures with finite variation
- Weakly compactly generated Banach lattices
- A weak$^*$ separable $C(K)^*$ space whose unit ball is not weak$^*$ separable
- Weak Compactness and Vector Measures
- The Range of a Vector Measure Determines its Total Variation
- A new class of weakly countably determined Banach spaces
- Weak Cauchy Sequences in L 1 (E)
- Pettis integral and measure theory
- Compactness and Weak Compactness in Spaces of Compact-Range Vector Measures
- Reflexivity and Order Properties of Scalar-Type Spectral Operators in Locally Convex Spaces
- Limited Operators and Strict Cosingularity
- Slicings, Selections and Their Applications
- Limited Sets in C(K)‐Spaces and Examples Concerning the Gelfand‐Phillips‐Property
- A Characterization of Banach Spaces Containing l 1
- Shorter Notes: L 1 x is Weakly Compactly Generated if x is
- An averaging property of the range of a vector measure
- Unconditional bases and martingales in LP(F)
- Remarks on the range of a vector measure
- Derivability, variation and range of a vector measure
- On Pettis integrals with separable range
- ON BOREL SETS IN FUNCTION SPACES WITH THE WEAK TOPOLOGY
- Banach Space Properties of L 1 of a Vector Measure