African Diaspora Journal of Mathematics

An Application of Ultrafilters to the Haar Measure

A. Maleki

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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 $\ell_{\infty}^{\star}(X)$.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 14, Number 1 (2012), 54-64.

Dates
First available in Project Euclid: 18 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1374153555

Mathematical Reviews number (MathSciNet)
MR3080396

Zentralblatt MATH identifier
1277.43001

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

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

Citation

Maleki, A. An Application of Ultrafilters to the Haar Measure. Afr. Diaspora J. Math. (N.S.) 14 (2012), no. 1, 54--64. https://projecteuclid.org/euclid.adjm/1374153555


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