Displaying similar documents to “Measurability of functions with approximately continuous vertical sections and measurable horizontal sections”

Exceptional directions for Sierpiński's nonmeasurable sets

B. Kirchheim, Tomasz Natkaniec (1992)

Fundamenta Mathematicae

Similarity:

In [2] the question was considered in how many directions can a nonmeasurable plane set behave even "better" than the classical one constructed by Sierpiński in [6], in the sense that any line in a given direction intersects the set in at most one point. We considerably improve these results and give a much sharper estimate for the size of the sets of those "better" directions.

An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions

J. Cichoń, Michał Morayne (1993)

Fundamenta Mathematicae

Similarity:

We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass...

Uniformly completely Ramsey sets

Udayan Darji (1993)

Colloquium Mathematicae

Similarity:

Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also...

Measures on compact HS spaces

Mirna Džamonja, Kenneth Kunen (1993)

Fundamenta Mathematicae

Similarity:

We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of 2 ω 1 . The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a G δ . A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.