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Some Selection Theorems for Measurable Functions

Published online by Cambridge University Press:  20 November 2018

C. J. Himmelberg  and
F. S. Van vleck
C. J. Himmelberg
Affiliation:
University of Kansas, Lawrence, Kansas
F. S. Van vleck
Affiliation:
University of Kansas, Lawrence, Kansas
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 394 - 399
Copyright
Copyright © Canadian Mathematical Society 1969

References

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