African Diaspora Journal of Mathematics

An Application of Ultrafilters to the Haar Measure

A. Maleki

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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

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

First available in Project Euclid: 18 July 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Maleki, A. An Application of Ultrafilters to the Haar Measure. Afr. Diaspora J. Math. (N.S.) 14 (2012), no. 1, 54--64.

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