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Measure-Theoretic Quantifiers and Haar Measure [PDF]
Proceedings of the American Mathematical Society, 1982 Measure-theoretic quantifiers are introduced as convenient notation and to facilitate certain applications of Fubini’s theorem. They are used to prove the uniqueness of Haar measure and to give some conditions involving translation which imply absolute continuity of another measure.
Russell Lyons
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Haar measure for measure groupoids [PDF]
Transactions of the American Mathematical Society, 1978 It is proved that Mackey’s measure groupoids possess an analogue of Haar measure for locally compact groups; and many properties of the group Haar measure generalize. Existence of Haar measure for groupoids permits solution of a question raised by Ramsay. Ergodic groupoids with finite Haar measure are characterized.
Peter Hahn
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Metric invariance of Haar measure [PDF]
Proceedings of the American Mathematical Society, 1983 Let d d be a left invariant metric for a locally compact group
Christoph Bandt
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A Property of the Haar Measure of Some Special LCA Groups [PDF]
Journal of Sciences, Islamic Republic of Iran, 2006 The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR.
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Irregular Invariant Measures Related to Haar Measure [PDF]
Proceedings of the American Mathematical Society, 1970 Let G be a locally compact nondiscrete group, and let ν
H. LeRoy Peterson
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A SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS [PDF]
Journal of Sciences, Islamic Republic of Iran, 2002 In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.
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The Haar measure and the generation of random unitary matrices [PDF]
, 2004 This paper derives the Haar measure over the set of unitary matrices. The Haar measure is essential when studying the statistical behavior of complex sample covariance matrices in terms of their eigenvalues and eigenvectors. The characterization is based
Svensson, Lennart,, Lundberg, Magnus,
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Visual Homing Navigation With Haar-Like Features in the Snapshot
IEEE Access, 2018 Visual homing navigation has been a challenging issue in indoor localization and navigation. Inspired by insect navigation, the snapshot model was introduced for homing navigation, where a pair of snapshots at the current location and at the nest are ...
Changmin Lee, Daeeun Kim
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New Journal of Physics, 2021 The distribution of entanglement of typical multiparty quantum states is not uniform over the range of the measure utilized for quantifying the entanglement.
George Biswas +2 more
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A Generalized Bohr–Jessen Type Theorem for the Epstein Zeta-Function
Mathematics, 2022 Let Q be a positive defined n×n matrix and Q[x̲]=x̲TQx̲. The Epstein zeta-function ζ(s;Q), s=σ+it, is defined, for σ>n2, by the series ζ(s;Q)=∑x̲∈Zn\{0̲}(Q[x̲])−s, and is meromorphically continued on the whole complex plane.
Antanas Laurinčikas, Renata Macaitienė
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