From: "G. A. Edgar" <edgar@math.ohio-state.edu.nospam>
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
<neum@cma.univie.ac.at> 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)