Complete Multi-Representations of Sets in a Computable Measure Space

TL;DR

This paper extends the understanding of multi-representations of measurable sets in computable measure spaces by establishing their recursive completeness concerning measure computability and set operations.

Contribution

It demonstrates that the previously introduced topologically complete representations are also recursively complete for measure and set-theoretic operations.

Findings

Multi-representations are topologically complete.

They are also recursively complete for measure computation.

They support computability of set-theoretic operations.

Abstract

In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them recursively complete w.r.t. computability of measure and set-theoretical operations.