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Some properties of step-functions connected with extension of measures. (English) Zbl 1181.28001
Summary: A step-function is any real-valued function whose range is (at most) countable. We discuss some measurability properties of step-functions formulated in terms of extensions of measure. The case of invariant (quasiinvariant) measures is considered especially. We show that this case essentially differs from the case of ordinary measures.
MSC:
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28D05 Measure-preserving transformations
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