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Start Over Subject Lebesgue measure

2. Statistical convergence of subsequences of a given sequence

Creator:
Mačaj, M. and Šalát, T.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
asymptotic density, statistical convergence, Lebesgue measure, Hausdorff dimension, and Baire category
Language:
English
Description:
This paper is closely related to the paper of Harry I. Miller: Measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811–1819 and contains a general investigation of statistical convergence of subsequences of an arbitrary sequence from the point of view of Lebesgue measure, Hausdorff dimensions and Baire’s categories.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. What’s the price of a nonmeasurable set?

Creator:
Sardella, Mirko and Ziliotti, Guido
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Lebesgue measure, nonmeasurable set, and axiom of choice
Language:
English
Description:
In this note, we prove that the countable compactness of {0, 1} R together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of . This is done by providing a family of nonmeasurable subsets of whose intersection with every non-negligible Lebesgue measurable set is still not Lebesgue measurable. We develop this note in three sections: the first presents the main result, the second recalls known results concerning non-Lebesgue measurability and its relations with the Axiom of Choice, the third is devoted to the proofs.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public