Speaker
Takis Konstantopoulos, Department of Mathematics, Uppsala University, Sweden
Topic
On the Extendibility of Finitely Exchangeable Probability Measures
Abstract
We
give
necessary
and
sufficient
conditions
in
order
that
a
finite
sequence
of
exchangeable
random
variables
in
a
fairly
general
state
space
be
extendible
to
a
longer
finite
or
to
an
infinite
exchangeable
sequence.
This
is
done
by
formulating
the
extendibility
problem
as
the
extension
problem
for
certain
bounded
linear
functionals
on
suitable
normed
spaces
and
by
using
the
Hahn-Banach
theorem
and
other
functional
measure-theoretic
techniques.
We
examine
when
such
a
finitely
exchangeable
random
sequence
is
a
mixture
(with
respect
to
a
probability
measure)
of
product
measures
and
also
study
the
preservation
of
the
extendibility
property
under
suitable
limiting
operations.
Invited by Professor Andrew Heunis