A short proof of an existence theorem in constructive measure theory

Abstract

The most important example of an integration space in the constructive measure theory of Bishop and Cheng is the couple $(X,\mu )$, where $X$ is a locally compact metric space and $\mu$ is a nonnegative linear function on the space of continuous functions of compact support on $X$. Bishop and Cheng’s proof that $(X,\mu )$ is indeed an integration space is rather involved. In this paper a much simpler proof is given.