Klaus Weihrauch ; Nazanin Tavana-Roshandel - Representations of measurable sets in computable measure theory

lmcs:1022 - Logical Methods in Computer Science, August 19, 2014, Volume 10, Issue 3 - https://doi.org/10.2168/LMCS-10(3:7)2014
Representations of measurable sets in computable measure theory

Authors: Klaus Weihrauch ; Nazanin Tavana-Roshandel

This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly countably infinite, over some alphabet {\Sigma}. As a basic computability structure we consider a computable measure on a computable $\sigma$-algebra. We introduce and compare w.r.t. reducibility several natural representations of measurable sets. They are admissible and generally form four different equivalence classes. We then compare our representations with those introduced by Y. Wu and D. Ding in 2005 and 2006 and claim that one of our representations is the most useful one for studying computability on measurable functions.

Volume: Volume 10, Issue 3
Published on: August 19, 2014
Accepted on: June 25, 2015
Submitted on: December 18, 2013
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic


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