Displaying similar documents to “Large equivalence of d h -measures.”

Spaces of σ-finite linear measure

Ihor Stasyuk, Edward D. Tymchatyn (2013)

Colloquium Mathematicae

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Spaces of finite n-dimensional Hausdorff measure are an important generalization of n-dimensional polyhedra. Continua of finite linear measure (also called continua of finite length) were first characterized by Eilenberg in 1938. It is well-known that the property of having finite linear measure is not preserved under finite unions of closed sets. Mauldin proved that if X is a compact metric space which is the union of finitely many closed sets each of which admits a σ-finite linear...

Thin and fat sets for doubling measures in metric spaces

Tuomo Ojala, Tapio Rajala, Ville Suomala (2012)

Studia Mathematica

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We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.

Singular measures and the key of G.

Stephen M. Buckley, Paul MacManus (2000)

Publicacions Matemàtiques

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We construct a sequence of doubling measures, whose doubling constants tend to 1, all for which kill a G set of full Lebesgue measure.

A characterization of the invertible measures

A. Ülger (2007)

Studia Mathematica

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Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.

Some properties of the Hausdorff distance in metric spaces.

Jozef Banas, Antonio Martinón (1990)

Extracta Mathematicae

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Some properties of the Hausdorff distance in complete metric spaces are discussed. Results obtained in this paper explain ideas used in the theory of measures of noncompactness.

Fubini’s Theorem on Measure

Noboru Endou (2017)

Formalized Mathematics

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The purpose of this article is to show Fubini’s theorem on measure [16], [4], [7], [15], [18]. Some theorems have the possibility of slight generalization, but we have priority to avoid the complexity of the description. First of all, for the product measure constructed in [14], we show some theorems. Then we introduce the section which plays an important role in Fubini’s theorem, and prove the relevant proposition. Finally we show Fubini’s theorem on measure.