Abstract
AbstractWe study invariant measures on compact Hausdorff spaces using finitary integral logic. For each compact Hausdorff space X and any family \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal F$\end{document} of its continuous transformations, we find equivalent conditions for the existence of an \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal F$\end{document}‐invariant measure on X. We give two proofs of the existence of Haar measure on compact groups.
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