Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic
Anatolij Dvurečenskij (1988)
Annales de l'I.H.P. Physique théorique
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Displaying similar documents to “Gleason theorem for signed measures with infinite values”
Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic
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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.
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Every conical measure on a weak complete space is represented as integration with respect to a -additive measure on the cylindrical -algebra in . The connection between conical measures on and -valued measures gives then some sufficient conditions for the representing measure to be finite.