Computability of measurable sets via effective topologies |
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Authors: | Yongcheng Wu Decheng Ding |
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Institution: | (1) Department of Mathematics, Nanjing University of Information Science and Technology, 210044 Nanjing, China;(2) Department of Mathematics, Nanjing University, 210093 Nanjing, China |
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Abstract: | We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure
space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability
results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite
computable measure space, and analyze the computability of the considered functions via respectively each of the standard
representations of the computable topological spaces constructed.
The authors are supported by grants of NSFC and DFG. |
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Keywords: | TTE Computability Measure Measurable set computable topological space |
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