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Bernstein sets with algebraic properties

100%

Kysiak M.

Open Mathematics

2009

tom 7

nr 4

725-731

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.

Spaces of measurable functions

84%

Niemiec P.

Open Mathematics

2013

tom 11

nr 7

1304-1316

For a metrizable space X and a finite measure space (Ω, $\mathfrak{M}$, µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of $\mathfrak{M}$-measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.

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2 Open Mathematics

1 Kysiak M.

1 Niemiec P.

1 2013

1 2009

Wyniki wyszukiwania

Bernstein sets with algebraic properties

Spaces of measurable functions