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CATEGORIES:Analysis Seminar
SUMMARY:The Steinhaus-Weil property: its converse\, Soleck
i amenability and subcontinuity - Adam Ostaszewski
\, The London School of Economics and Political Sc
ience
DTSTART:20161128T160000Z
DTEND:20161128T170000Z
UID:TALK2133AT
URL:/talk/index/2133
DESCRIPTION:The Steinhaus-Weil theorem that concerns us is the
`interior points' property -- that in a topologic
al group a non-negligible set S has the identity a
s an interior point of S⁻¹S. There are various con
verses\; the one that mainly concerns us is due to
Simmons and Mospan. Here the group is locally com
pact\, so we have a Haar reference measure η. The
Simmons-Mospan theorem states that a (regular Bore
l) measure has such a Steinhaus-Weil property if a
nd only if it is absolutely continuous with respec
t to the Haar measure. We exploit the connection
between the interior points property and a selecti
ve form of infinitesimal invariance afforded by a
certain family of selective reference measures σ\,
drawing on Solecki's amenability at 1 (and using
Fuller's notion of subcontinuity. We may thereby d
evelop a number of relatives of the Simmons-Mospan
theorem. This has links with topologies of Weil t
ype.
LOCATION:Lecture Theatre 1\, Strathcona Building
CONTACT:Andrew Morris
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