# Pettis integral and measure theory

@inproceedings{Talagrand1984PettisIA,
title={Pettis integral and measure theory},
author={Michel Talagrand},
year={1984}
}
223 Citations
On Pettis integral and Radon measures
Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This
Tame functionals on Banach algebras
In the present note we introduce tame functionals on Banach algebras. A functional $f \in A^*$ on a Banach algebra $A$ is tame if the naturally defined linear operator $A \to A^*, a \mapsto f \cdot Pettis Integrability of Multifunctions with Values in Arbitrary Banach Spaces There is a rich literature describing integrability of multifunctions that take weakly compact convex subsets of a separable Banach space as their values. Most of the papers concern the Bochner type Some translation-invariant Banach function spaces which contain$c_0$• Mathematics • 2004 We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space$c_0$. COMPACT RANGE PROPERTY AND OPERATORS • Mathematics • 2000 We prove that a Banach space E has the compact range property (CRP) if and only if, for any given C∗-algebra A, every absolutely summing operator from A into E is compact. Related results for A dichotomy property for locally compact groups • Mathematics Journal of Functional Analysis • 2018 The Ascoli property for function spaces and the weak topology of Banach and Fr\'echet spaces • Mathematics • 2015 Following [3] we say that a Tychonoff space$X$is an Ascoli space if every compact subset$\mathcal{K}$of$C_k(X)$is evenly continuous; this notion is closely related to the classical Ascoli Representations of dynamical systems on Banach spaces not containing$l_1$• Mathematics • 2008 For a topological group G, we show that a compact metric G-space is tame if and only if it can be linearly represented on a separable Banach space which does not contain an isomorphic copy of$l_1\$
The Birkhoff integral and the property of Bourgain
• Mathematics
• 2005
Abstract.In this paper we study the Birkhoff integral of functions f:Ω→X defined on a complete probability space (Ω,Σ,μ) with values in a Banach space X. We prove that if f is bounded then its