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Nonmeasurable algebraic sums of sets of reals

Marcin Kysiak — 2005

Colloquium Mathematicae

We present a theorem which generalizes some known theorems on the existence of nonmeasurable (in various senses) sets of the form X+Y. Some additional related questions concerning measure, category and the algebra of Borel sets are also studied.

Bernstein sets with algebraic properties

Marcin Kysiak — 2009

Open Mathematics

We construct Bernstein sets in ℝ having some additional algebraic properties. In particular, solving a problem of Kraszewski, Rałowski, Szczepaniak and Żeberski, we construct a Bernstein set which is a < c-covering and improve some other results of Rałowski, Szczepaniak and Żeberski on nonmeasurable sets.

Some Remarks on Indicatrices of Measurable Functions

Marcin Kysiak — 2005

Bulletin of the Polish Academy of Sciences. Mathematics

We show that for a wide class of σ-algebras 𝓐, indicatrices of 𝓐-measurable functions admit the same characterization as indicatrices of Lebesgue-measurable functions. In particular, this applies to functions measurable in the sense of Marczewski.

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