Pettis integral and measure theory

  title={Pettis integral and measure theory},
  author={Michel Talagrand},
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 $c_0$
We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$.
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
The Ascoli property for function spaces and the weak topology of Banach and Fr\'echet spaces
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 $l_1$
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
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