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Some Selection Theorems for Measurable Functions
- Source :
- Canadian Journal of Mathematics. 21:394-399
- Publication Year :
- 1969
- Publisher :
- Canadian Mathematical Society, 1969.
-
Abstract
- Let F: X → Y be a multifunction from X to Y. Then, given measure-theoretic or topological structures on X and Y, it is possible in various ways to define the measurability of F. The selection problem is to determine which structures on X and Y and which definitions of measurability of F ensure that F will have a measurable selector. This problem has been studied recently in papers by Castaing (2) and Kuratowski and Ryll-Nardzewski (6). In the latter paper, the problem is studied for its own interest. The former uses solutions of the problem to obtain general Filippov-type theorems. (See, for example, the corollaries following Theorems 2 and 3 of Castaing's paper.) For other material on Filippov's results see, among others, (3; 4; 5; 7; 9).
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 21
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........66ca33924f192caf4eb3f0a731f86abb