From: Ronald Bruck <bruck@math.usc.edu>
Subject: Re: Campaign to rename L_p spaces
Date: Fri, 08 Sep 2000 13:09:43 -0700
Newsgroups: sci.math
Summary: [missing]

In article <39b93502.1473960@news.iperbole.bologna.it>, 
vis1918@iperbole.bologna.it (unafolla) wrote:

> On Fri, 08 Sep 2000 08:22:40 -0700, Ronald Bruck <bruck@math.usc.edu>
> wrote:
> 
> >In article <39B86F76.19E2D45A@math.missouri.edu>, Stephen 
> >Montgomery-Smith <stephen@math.missouri.edu> wrote:
> >
> >
> >Why restrict it to sigma-finite?  The dual of L^p is L^q whether the 
> >measure space is sigma-finite or not (for 1 < p < \infty).  A nice 
> >exercise, not usually done in most real-analysis courses (perhaps 
> >because it's not of much practical value).  Hint:  the support of an L^p 
> >function is sigma-finite...
> >
> 
> Could someone explain me what "sigma finite" means and what is about?
> Thanks in advance.
> Bye

It means "a countable union of sets of finite measure".  Example:  R^n, 
with Lebesgue measure, is sigma-finite, because it can be written as the 
union of balls of radius m for m = 1, 2, 3, ..., and each such ball has 
finite Lebesgue measure.

--Ron Bruck

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