Document Type
Lecture
Publication Date
9-24-2009
Abstract
Let μ be a measure from a σ-algebra of subsets of a set �� into a sequentially complete Hausdorff topological vector space ��. Assume that the convex hull of the range of μ is bounded in �� and denote by L₁(μ) the space of scalar-valued functions on �� that are integrable with respect to the vector measure μ. Sometimes a property of �� is inherited by L₁(μ). I will show that the bounded multiplier property passes from �� to L₁(μ). Answering a 1972 question of Erik Thomas, I will show that for a large class of F-spaces ��, the non-containment of c₀ passes onto L₁(μ). Students are welcome. An attempt will be made at explaining the notions and the theory of integration with respect to a vector measure.
Relational Format
presentation
Recommended Citation
Labuda, Iwo, "Geometry of L₁(μ) for Vector-Valued Measure, Part I" (2009). Analysis Seminar. 34.
https://egrove.olemiss.edu/math_analysis/34
