The Haar measure problem
Copyright policy )The Haar measure problem
An old problem asks whether every compact group has a Haar-nonmeasurable subgroup. A series of earlier results reduce the problem to infinite metrizable profinite groups. We provide a positive answer, assuming a weak, potentially provable, consequence of the Continuum Hypothesis. We also establish the dual, Baire category analogue of this result.
To appear in Proceedings of the AMS
- Bar-Ilan University Israel
- Warsaw University of Life Sciences Poland
- University of Warsaw Poland
- Cardinal Stefan Wyszyński University in Warsaw Poland
continuum hypothesis, subgroup, General Topology (math.GN), Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Mathematics - Logic, Compact groups, Cardinal characteristics of the continuum, Functional Analysis (math.FA), measurable, Mathematics - Functional Analysis, unconditionally closed sets, profinite, symbolic dynamics, Markov, FOS: Mathematics, Cantor groups, group, Set functions and measures on topological groups or semigroups, Haar measures, invariant measures, Logic (math.LO), Mathematics - General Topology
continuum hypothesis, subgroup, General Topology (math.GN), Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Mathematics - Logic, Compact groups, Cardinal characteristics of the continuum, Functional Analysis (math.FA), measurable, Mathematics - Functional Analysis, unconditionally closed sets, profinite, symbolic dynamics, Markov, FOS: Mathematics, Cantor groups, group, Set functions and measures on topological groups or semigroups, Haar measures, invariant measures, Logic (math.LO), Mathematics - General Topology
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