Campus Units

Computer Science, Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

2019

Journal or Book Title

Fundamenta Mathematicae

Volume

244

First Page

255

Last Page

285

DOI

10.4064/fm448-5-2018

Abstract

We continue the investigation of analytic spaces from the perspective of computable structure theory. We show that if p ≥ 1 is a computable real, and if Ω is a nonzero, non-atomic, and separable measure space, then every computable presentation of Lᵖ(Ω) is computably linearly isometric to the standard computable presentation of Lᵖ[0, 1]; in particular, Lᵖ[0, 1] is computably categorical. We also show that there is a measure space Ω that does not have a computable presentation even though Lᵖ(Ω) does for every computable real p ≥ 1.

Comments

This is a manuscript of an article published as Clanin, Joe, Timothy H. McNicholl, and Don M. Stull. "Analytic computable structure theory and Lp spaces." Fundamenta Mathematicae 244 (2019): 255-285. doi: 10.4064/fm448-5-2018. Posted with permission.

Copyright Owner

Institute of Mathematics, Polish Academy of Sciences

Language

en

File Format

application/pdf

Published Version

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