Results 11 to 20 of about 2,437,555 (245)
CoRR, 2021 We describe the formalization of the existence and uniqueness of the Haar measure in the Lean theorem prover. The Haar measure is an invariant regular measure on locally compact groups, and it has not been formalized in a proof assistant before.
van Doorn, Floris
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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.
Peter Hahn
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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 ...
Russell Lyons
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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 G G . We prove that isometric subsets of ( G , d ) (G,d) have equal Haar measure.
Christoph Bandt
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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 1 {\nu _1} be a Haar measure on an open subgroup of G G . It is not hard to show that ν 1
H. LeRoy Peterson
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CoRR, 2019 According to Haar's Theorem, every compact group $G$ admits a unique (regular, right and) left-invariant Borel probability measure $μ_G$. Let the Haar integral (of $G$) denote the functional $\int_G:\mathcal{C}(G)\ni f\mapsto \int f\,dμ_G$ integrating any continuous function $f:G\to\mathbb{R}$ with respect to $μ_G$.
Arno Pauly +2 more
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Proceedings of the American Mathematical Society, 2018 To appear in Proceedings of the ...
Adam Przeździecki +2 more
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Proceedings of the American Mathematical Society, 1955 Summary: Der Verf weist einleitend darauf hin, daß das Haar-Integral auf kompakten Gruppen, Vektor-Gruppen und diskreten Gruppen durch verhältnismäßig einfache, wohl bekannte Operationen erhalten wird. In Verallgemeinerung eines entsprechenden Satzes von \textit{G. D. Mostow} über Lie-Gruppen [Am. J. Math. 74, 920--928 (1952; Zbl 0049.35801)] und unter
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