## African Diaspora Journal of Mathematics

### An Application of Ultrafilters to the Haar Measure

A. Maleki

#### 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

Mathematical Reviews number (MathSciNet)
MR3080396

Zentralblatt MATH identifier
1277.43001

#### 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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