From: "G. A. Edgar"
Subject: Re: invariant measure on infinite-dimensional sphere
Date: 5 Jul 1999 12:30:02 -0500
Newsgroups: sci.math.research,sci.math
Keywords: cylindrical, Wiener measures
In article <37808319.A3C3291D@cma.univie.ac.at>, Arnold Neumaier
wrote:
> Can anyone tell me where I can read about invariant measures dm on
> spheres in infinite-dimensional real or complex space, and how to
> compute integrals \int f(x)dm for nice functions f?
>
> Please reply also to my email address, since I don't read news
> frequently.
>
> Arnold Neumaier
> neum@cma.univie.ac.at
> http://solon.cma.univie.ac.at/~neum/
There is no good analog for spaces like infinite-dimensional Hilbert
space. Probably the closest are the so-called cylindrical measures:
in the space itself, they are not countably additive, so they
should be thought of as living on a larger space.
Another type is where the measure is not supported on the whole
space, but only on a subspace. An good example of this is known
as Wiener measure (or Brownian motion).
--
Gerald A. Edgar edgar@math.ohio-state.edu
Department of Mathematics telephone: 614-292-0395 (Office)
The Ohio State University 614-292-4975 (Math. Dept.)
Columbus, OH 43210 614-292-1479 (Dept. Fax)