A Generalization of Steinhaus' Theorem and Some Nonmeasurable Sets

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.