Extreme topological measures

Volume 192 / 2006

S. V. Butler Fundamenta Mathematicae 192 (2006), 141-153 MSC: 46E27, 28C15, 54F65. DOI: 10.4064/fm192-2-4


It has been an open question since 1997 whether, and under what assumptions on the underlying space, extreme topological measures are dense in the set of all topological measures on the space. The present paper answers this question. The main result implies that extreme topological measures are dense on a variety of spaces, including spheres, balls and projective planes.


  • S. V. ButlerDepartment of Mathematics
    University of Illinois at Urbana-Champaign
    273 Altgeld Hall, 1409 West Green Street
    Urbana, IL 61801, U.S.A.

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