Document Type
Lecture
Publication Date
2-27-2010
Abstract
We start by solving an exercise about measurability that requires knowledge of a basic course of measure theory. From here we review the views of Fréchet about the Lebesgue integral and recall the notions of Bochner and Pettis integrability. The second part of the lecture touches on topics in ongoing research: we show how a modification of the ideas in the starting exercise is used to provide a characterization of Birkhoff integrability that lies nicely between Bochner and Pettis integrability: Birkhoff integrability can be defined via limits of Riemann-type sums. Another modification in the exercise is used to prove an extension of the classical Kuratowski and Ryll-Nardzewski selection theorem about the existence of measurable selectors for multifunctions. The latter is applied to the theory of integration of multifunctions.
Relational Format
presentation
Recommended Citation
Cascales, Bernardo, "Scalar, vector and multi-valued integration" (2010). Colloquium. 42.
https://egrove.olemiss.edu/math_colloquium/42
