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

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.