Disintegration and perfectness of measure spaces.

Monika Remy

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Displaying similar documents to “Disintegration and perfectness of measure spaces.”

Problems of Number and Measure

Robert Morris Pierce

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Fubini’s Theorem on Measure

Noboru Endou (2017)

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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.

On the Extremality of measure extensions.

D. Bierlein, W.J.A. Stich (1989)

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Product Pre-Measure

Noboru Endou (2016)

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In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from σ-measure because existence of σ-measure on any semialgebras has been proved in [15]. In this approach, we use some theorems for integrals.

Correction to the paper "Two classes of measures''

Jan K. Pachl (1981)

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A classification of measure spaces

Robert E. Zink (1966)

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A problem of invariance for Lebesgue measure

James Fickett, Jan Mycielski (1979)

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A characterization of the invertible measures

A. Ülger (2007)

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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.

Differentiation of measures.

Ricardo Faro Rivas, Juan A. Navarro, Juan Sancho (1994)

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Construction of Measure from Semialgebra of Sets1

Noboru Endou (2015)

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In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore,...