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Extending Invariant Measures on Topological Groups a
Author(s) -
ZAKRZEWSKI PIOTR
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb36817.x
Subject(s) - mathematics , uncountable set , hausdorff space , invariant (physics) , countable set , locally compact space , bounded function , pure mathematics , second countable space , discrete mathematics , combinatorics , topology (electrical circuits) , mathematical analysis , mathematical physics
Let G be an uncountable Hausdorff topological group. We prove that if G is either Polish and not locally compact or compact and not zero‐dimensional, or the countable product of finite groups with uniformly bounded cardinalities, then every invariant s̀‐finite measure on G has a proper invariant extension. We do this by expressing G as the union of a “short” chain of its proper subgroups.