A short proof of an existence theorem in constructive measure theory
Author: Y. K. Chan
Journal: Proc. Amer. Math. Soc. 48 (1975), 435-437
MSC: Primary 28A30; Secondary 02E99
MathSciNet review: 0364590
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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.
E. Bishop and H. Cheng, Constructive measure theory, Mem. Amer. Math. Soc. No. 116 (1972).