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2012 An Application of Ultrafilters to the Haar Measure
A. Maleki
Afr. Diaspora J. Math. (N.S.) 14(1): 54-64 (2012).

Abstract

In this article we will use ultrafilter theory to present a modified proof that a locally compact group with a countable basis has a left invariant and a right invariant Haar measure. To facilitate this result, we shall first show that the topological space consisting of all ultrafilters on a nonempty set $X$ is homeomorphic to the topological space of all nonzero multiplicative functionals in the first dual space $\ell_{\infty}^{\star}(X)$.

Citation

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A. Maleki. "An Application of Ultrafilters to the Haar Measure." Afr. Diaspora J. Math. (N.S.) 14 (1) 54 - 64, 2012.

Information

Published: 2012
First available in Project Euclid: 18 July 2013

zbMATH: 1277.43001
MathSciNet: MR3080396

Subjects:
Primary: 22Bxx, 22Cxx, 22Dxx, 22Exx,28Axx, 28Cxx, and 28Exx

Keywords: Banach Algebra , Borel Set and Invariant Measure , Homomorphism , Locally Compact , Topological Group , Ultrafilter

Rights: Copyright © 2012 Mathematical Research Publishers

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Vol.14 • No. 1 • 2012
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