The Ghahramani-Lau conjecture is established; in other words, the measure algebra of every locally compact group is strongly Arens irregular. To this end, we introduce and study certain new classes of measures (called approximately invariant, respectively, strongly singular) which are of interest in their own right. Moreover, we show that the same result holds for the measure algebra of any (not necessarily locally compact) Polish group.

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Keywords Arens product, Locally compact group, Measure algebra, Separation of measures, Thin measure, Topological centre
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Journal Advances in Mathematics
Losert, V. (Viktor), Neufang, T, Pachl, J. (Jan), & Steprans, J. (Juris). (2016). Proof of the Ghahramani-Lau conjecture. Advances in Mathematics, 290, 709–738. doi:10.1016/j.aim.2015.12.004