Displaying similar documents to “A note on strictly positive Radon measures”

On a one-dimensional analogue of the Smale horseshoe

Ryszard Rudnicki (1991)

Annales Polonici Mathematici

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We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have ∫ φ ( T n x ) f ( x ) d x → ∫ φ d μ , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then n - 1 ∑ i = 0 n - 1 φ ( T i x ) → ∫ φ d μ for Lebesgue-a.e. x.

Measures on compact HS spaces

Mirna Džamonja, Kenneth Kunen (1993)

Fundamenta Mathematicae

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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.

A new proof of Kelley's Theorem

S. Ng (1991)

Fundamenta Mathematicae

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Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.

Exceptional directions for Sierpiński's nonmeasurable sets

B. Kirchheim, Tomasz Natkaniec (1992)

Fundamenta Mathematicae

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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.

Weakly α-favourable measure spaces

David Fremlin (2000)

Fundamenta Mathematicae

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I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.

Quantitative Isoperimetric Inequalities on the Real Line

Yohann de Castro (2011)

Annales mathématiques Blaise Pascal

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In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown that, in the Gauss space, a set of given measure and almost minimal Gauss boundary measure is necessarily close to be a half-space. Using only geometric tools, we extend their result to all symmetric log-concave measures on the real line. We give sharp quantitative isoperimetric inequalities and prove that among sets of given measure and given asymmetry (distance to half line, i.e. distance to sets...