A Generalization of Steinhaus' Theorem and Some Nonmeasurable Sets

Robert Rałowski, Przemysław Szczepaniak, Szymon Żeberski

Type: Article

Publication Date: 2010-01-01

Citations: 3

DOI: https://doi.org/10.14321/realanalexch.35.2.0403

Abstract

We generalize a classical Steinhaus theorem replacing addition by any two variable function which is differentiable. We deal with category and measure case. Measure case was done before in papers [3], [9]. We give a proof which can be easily generalized to category case. We also obtain a variety of examples of nonmeasurable sets which have interesting algebraic properties.

Locations

Real Analysis Exchange - View - PDF

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