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Let (X, 3, v) be an internal measure space in a denumerably comprehensive enlargement. The set X is a standard measure space when equipped with the smallest standard o-algebra % containing the algebra a, where the extended real-valued measure p. on % is generated by the standard part of v. If / is fl-measurable, then its standard part / is jR-measurable on X. If / and p. are finite, then the vintegral of / is infinitely close to the /¿-integral of /. Applications include coin tossing anddoi:10.1090/s0002-9947-1975-0390154-8 fatcat:ha32s7tpizgnzbjzweovyeboqi