Very excited about this new preprint with Kyle Gannon and Krzysztof Krupinski! "Definable convolution and idempotent Keisler measures III. Generic stability, generic transitivity, and revised Newelski's conjecture" arxiv.org/abs/2406.00912#ModelTheory#math

Definable convolution and idempotent Keisler measures III. Generic...

We study idempotent measures and the structure of the convolution semigroups of measures over definable groups. We isolate the property of generic transitivity and demonstrate that it is...

Classical work by Wendel, Rudin, Cohen (before inventing forcing) and others classifies idempotent Borel measures on locally compact abelian groups, showing that they are precisely the Haar measures of compact subgroups.