Applications
Immediately after publishing the Haar theorem, it was used to solve Hilbert's fifth problem which concerns the characterization of Lie groups. Haar measures apply more generally to two fields of mathematics, abstract harmonial analysis and mathematical statistics.
In abstract harmonial analysis, Haar measures are used on locally compact groups, especially with Pontryagin duality. For more on harmonial analysis: https://en.wikipedia.org/wiki/Harmonic_analysis#Abstract_harmonic_analysis
