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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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