.
Invariant Measures for Amenable Locally
Compact Groups and Hypergroups
Doctor Ben Willson
Western Illinois University
Abstract: The standard Lebesgue measure on the real line is
translation invariant. That is,
Z
Z
f (x + a) dx for any a. In fact, every
f (x) dx =
R
R
locally compact group G has a unique translation invariant
regular Borel measure.
This measure can be considered as an element in the
order dual of CC (G), the bounded continuous functions
on G with compact support. Every amenable group has
a translation invariant mean in the dual of the space of
continuous bounded functions, C(G).
The ideas of translation invariant measures and means
can be extended to hypergroups (locally compact spaces
with a convolution product on the probability measures).
Whether every hypergroup admits a translation invariant
measure is a longstanding open problem. In this talk, I will
discuss some of the background and present a partial answer;
that amenable hypergroups with a certain property always
have a translation invariant measure.
DEPARTMENT
of
MATHEMATICS
Thursday,
December 10, 2015
3:45 p.m.
Morgan Hall 204
Refreshments
will be served at 3:30
p.m.