Wednesday, February 3, 2021 - 12:30 in ZOOM - Video Conference
Approximation of measures by finite-dimensional projections
A talk in the Bielefeld Stochastic Afternoon series by
Vladimir Bogachev from Moscow State University, Russia
| Abstract: |
We are so much accustomed to the fact that, given a Borel probability measure $\mu$ on a separable Banach or Fréchet space $X$, there is a sequence of finite-dimensional projections of $\mu$, i.e., its images under continuous finite-dimensional operators on $X$, weakly convergent to $\mu$.
From introductory courses on infinite-dimensional integration we vaguely remember that this must be true in Hilbert spaces and in the space $\mathbb{R}^\infty$ of all sequences, and a clear evidence seems to be provided by another fact: the measure $\mu$ is uniquely determined by its
finite-dimensional projections.
There is no doubt about the latter fact, but is the former one really true?
It will be shown in my talk that this is not a question of the sort one poses after a prolonged celebration of New Year and Christmas along with the
Russian Old New Year.
Of course, bases and stochastic bases will appear in our discussion.
Some related interesting results and questions will be presented.
No prerequisites are needed except for acquaintance with basic concepts of Banach spaces and Borel measures.
Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password.
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