Let A ⊆ω2 be measurable. The density set DA is the set of Z ∈ω2 such that the local measure of A along Z tends to 1. Suppose that A is a Π10 set with empty interior and the uniform measure of A is a positive computable real. We show that DA is lightface Π30 complete for effective Wadge reductions. This is an algorithmic version of a result in descriptive set theory by Andretta and Camerlo [1]. They show a completeness result for boldface Π30 sets under plain Wadge reductions.
Lightface Π03-completeness of density sets under effective wadge reducibility
Carotenuto, Gemma;
2016-01-01
Abstract
Let A ⊆ω2 be measurable. The density set DA is the set of Z ∈ω2 such that the local measure of A along Z tends to 1. Suppose that A is a Π10 set with empty interior and the uniform measure of A is a positive computable real. We show that DA is lightface Π30 complete for effective Wadge reductions. This is an algorithmic version of a result in descriptive set theory by Andretta and Camerlo [1]. They show a completeness result for boldface Π30 sets under plain Wadge reductions.File in questo prodotto:
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