Abstract
The Loeb measure construction from nonstandard analysis is applied to two theorems in standard measure theory. In both cases the essential simplification offered by the approach is the ability to work with a σ-additive measure space, even if the hypotheses only guarantee finite additivity. The key to this simplification is the property of \({\aleph_1}\)-saturated nonstandard models, that any finitely additive measure on an internal algebra extends immediately to a σ-additive measure.
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