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A functional approach to nonstandard measure theory. (English) Zbl 0533.28008
Contemp. Math. 26, 251-261 (1984).
In 1973, the author used the Carathéodory extension theorem to construct structurally rich, standard measure spaces on nonstandard point sets. This contruction has since been used by a number of researchers to obtain new results in many areas including measure and probability theory, potential theory, mathematical physics and mathematical economics. The author’s measure theory is simplified and extended in this paper by starting from first principles with an internal functional and constructing a standard representing measure.
For the entire collection see [Zbl 0523.00008].

MSC:
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
26E35 Nonstandard analysis
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