Displaying similar documents to “Invariant extensions of the Haar measure”

Invariant extension of Haar measure

Antal Járai

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CONTENTS§1. Introduction...............................................................5§2. Covariant extension of measures..............................6§3. An invariant extension of Haar measure..................15§4. Covariant extension of Lebesgue measure.............22References....................................................................26

Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension

Hélène Airault, Habib Ouerdiane (2011)

Banach Center Publications

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Consider a Lie group with a unitary representation into a space of holomorphic functions defined on a domain 𝓓 of ℂ and in L²(μ), the measure μ being the unitarizing measure of the representation. On finite-dimensional examples, we show that this unitarizing measure is also the invariant measure for some differential operators on 𝓓. We calculate these operators and we develop the concepts of unitarizing measure and invariant measure for an OU operator (differential operator...

Existence and integral representation of regular extensions of measures

Werner Rinkewitz (2001)

Colloquium Mathematicae

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Let ℒ be a δ-lattice in a set X, and let ν be a measure on a sub-σ-algebra of σ(ℒ). It is shown that ν extends to an ℒ-regular measure on σ(ℒ) provided ν*|ℒ is σ-smooth at ∅ and ν*(L) = inf ν*(U)|X ∖ U ∈ ℒ, Usupset L for all L ∈ ℒ. Moreover, a Choquet type representation theorem is proved for the set of all such extensions.

On the generalized Avez method

Antoni Leon Dawidowicz (1992)

Annales Polonici Mathematici

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A generalization of the Avez method of construction of an invariant measure is presented.