Archive for Mathematical Logic 45 (3):365-379 (2006)

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
Keywords TTE  Computability  Measure  Measurable set  computable topological space
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Reprint years 2005, 2006
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DOI 10.1007/s00153-005-0315-x
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On the Computability of Fractal Dimensions and Hausdorff Measure.Ker-I. Ko - 1998 - Annals of Pure and Applied Logic 93 (1-3):195-216.

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