Multilinear Lebesgue-Bochner-Stieltjes integral

Strong Barrelledness Properties in Lebesgue-Bochner Spaces

If (Ω,Σ, μ) is a finite atomless measure space and X is a normed space, we prove that the space Lp(μ,X), 1 ≤ p ≤ ∞ is a barrelled space of class א0, regardless of the barrelledness of X. That enables us to obtain a localization theorem of certain mappings defined in Lp(μ,X). By “space” we mean a “real or complex Hausdorff locally convex space”. Given a dual pair (E,F ), as usual σ(E,F ) denotes...

Rethinking the Lebesgue Integral

The near Radon-nikodym Property in Lebesgue-bochner Function Spaces

Let X be a Banach space and (Ω,Σ, λ) be a finite measure space, 1 ≤ p < ∞. It is shown that L(λ,X) has the Near Radon-Nikodym property if and only if X has it. Similarly if E is a Köthe function space that does not contain a copy of c0, then E(X) has the Near Radon-Nikodym property if and only if X does.

Extreme points of the unit cell Lebesgue-Bochner function spaces

On volumes generating the same lebesgue-bochner integration.

Introduction.-Let R,Y be the space of reals and a Banach space, respectively. The norm of elements in these spaces will be denoted by |. A nonempty family of sets V of an abstract space X will be called a pre-ring if for any two sets A,,A2a V we have Ai nA2G V, and there exist disjoint sets B1,..., BkEV such that A1\A2 = B1U ... UBt. A nonnegative finite-valued function v on the pre-ring V will...