Displaying similar documents to “Differentiation of measures.”

A characterization of the invertible measures

A. Ülger (2007)

Studia Mathematica

Similarity:

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.

Singular measures and the key of G.

Stephen M. Buckley, Paul MacManus (2000)

Publicacions Matemàtiques

Similarity:

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

Fubini’s Theorem on Measure

Noboru Endou (2017)

Formalized Mathematics

Similarity:

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.

Negligible sets and good functions on polydiscs

Kohur Gowrisankaran (1979)

Annales de l'institut Fourier

Similarity:

A notion of negligible sets for polydiscs is introduced. Some properties of non-negligible sets are proved. These results are used to construct good and good inner functions on polydiscs.

Product Pre-Measure

Noboru Endou (2016)

Formalized Mathematics

Similarity:

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.