Analytic computable structure theory and $L^p$-spaces part 2

TL;DR

This paper extends the classification of computable $L^p$ spaces with atomic measure spaces, analyzing their degrees of categoricity and the complexity of projection maps, advancing the understanding of their computability properties.

Contribution

It provides a classification of computable $L^p$ spaces with atomic but not purely atomic measure spaces and analyzes their degrees of categoricity.

Findings

Classified computable $L^p$ spaces with atomic measure spaces

Determined degrees of categoricity for these spaces

Analyzed complexity of associated projection maps

Abstract

Suppose $p \geq 1$ is a computable real. We extend previous work of Clanin, Stull, and McNicholl by classifying the computable $L^p$ spaces whose underlying measure spaces are atomic but not purely atomic. In addition, we determine the degrees of categoricity of these spaces and the complexity of associated projection maps.