Some properties of the density topology with respect to an extension of the Lebesgue measure.
Hejduk, Jacek (1998)
Mathematica Pannonica
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Displaying similar documents to “Some Non-Measurable Sets”
Some properties of the density topology with respect to an extension of the Lebesgue measure.
A topological proof of Denjoy-Stepanoff theorem
Jaroslav Lukeš (1978)
Časopis pro pěstování matematiky
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Pointwise density topology
Magdalena Górajska (2015)
Open Mathematics
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The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise...
On the Measurability of Functions of Two Variables
Roy O. Davies (1973)
Matematický časopis
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On topologies generated by some operators
Katarzyna Flak, Jacek Hejduk (2013)
Open Mathematics
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The paper concerns topologies introduced in a topological space (X, τ) by operators which are much weaker than the lower density operators. Some properties of the family of sets having the Baire property and the family of meager sets with respect to such topologies are investigated.
On the pointwise limits of sequences of Świątkowski functions
Tomasz Natkaniec, Julia Wódka (2018)
Czechoslovak Mathematical Journal
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The characterization of the pointwise limits of the sequences of Świątkowski functions is given. Modifications of Świątkowski property with respect to different topologies finer than the Euclidean topology are discussed.