Displaying similar documents to “Conical measures and vector measures”

Limits of inverse systems of measures

J. D. Mallory, Maurice Sion (1971)

Annales de l'institut Fourier

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In this paper the problem of the existence of an inverse (or projective) limit measure μ ' of an inverse system of measure spaces ( X i , μ i ) is approached by obtaining first a measure μ ˜ on the whole product space ∏ i ∈ I X i . The measure μ ˜ will have many of the properties of a limit measure provided only that the measures μ i possess mild regularity properties. It is shown that μ ' can only exist when μ ˜ is itself a “limit” measure in a more general sense, and that μ ' must then be the restriction...

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.