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The Spring Topology and Dynamics Conference 2009
March 7-9, 2009
University of Florida
Gainesville, FL, USA

Organizers
Lou Block, Phil Boyland (chair), Beverly Brechner, Sasha Dranishnikov, and Jed Keesling.

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There may be just continuum many universally measurable sets
by
Paul Larson
Miami University
Coauthors: Saharon Shelah

A subset of a topological space is said to be universally measurable if it is measurable with respect to every complete, countably additive sigma-finite measure on the space, and universally null if it has measure zero for each such atomless measure. In 1934, Hausdorff proved that there exist universally null sets of cardinality ℵ1, and thus that there exist at least 2ℵ1 such sets. Laver showed in the 1970's that consistently there are just continuum many universally null sets. The question of whether there exist more than continuum many universally measurable sets was asked by Mauldin in 1978. We show that consistently there exist only continuum many universally measurable sets.

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Date received: February 15, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxy-65.