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.
Copyright Owner
Institute of Mathematics, Polish Academy of Sciences
Copyright Date
2019
Language
en
File Format
application/pdf
Recommended Citation
Clanin, Joe; McNicholl, Timothy H.; and Stull, Don M., "Analytic computable structure theory and Lp spaces" (2019). Mathematics Publications. 262.
https://lib.dr.iastate.edu/math_pubs/262
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.