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A UNIFIED APPROACH TO CONTINUOUS, MEASURABLE SELECTIONS, AND SELECTIONS FOR HYPERSPACES

Part of: Set theory Classical measure theory Maps and general types of spaces defined by maps Set functions, measures and integrals with values in abstract spaces Basic constructions

Published online by Cambridge University Press:  21 May 2018

Fotis H. Mavridis
Fotis H. Mavridis*
Affiliation:
National Technical University of Athens, Department of Mathematics, Zografou Campus, 15780 Athens, Greece email [email protected]
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Abstract

In this paper we provide a unified approach, based on methods of descriptive set theory, for proving some classical selection theorems. Among them is the zero-dimensional Michael selection theorem, the Kuratowski–Ryll-Nardzewski selection theorem, as well as a known selection theorem for hyperspaces.

MSC classification

Primary: 54C65: Selections 54C60: Set-valued maps 54B20: Hyperspaces 28B20: Set-valued set functions and measures; integration of set-valued functions; measurable selections
Secondary: 03E15: Descriptive set theory 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
Type
Research Article
Information
Mathematika , Volume 64 , Issue 3 , 2018 , pp. 607 - 627
Copyright
Copyright © University College London 2018 

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Footnotes

This paper contains a part of the author’s doctoral thesis written under the supervision of Professor Alexander D. Arvanitakis at the National Technical University of Athens. The author would like to thank Professor Alexander Arvanitakis, Professor Apostolos Giannopoulos, Dr Elena Papanikolaou, and the referee for their valuable feedback.

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