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.
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 435-437
- MSC: Primary 28A30; Secondary 02E99
- DOI: https://doi.org/10.1090/S0002-9939-1975-0364590-5
- MathSciNet review: 0364590