Measures with finite mass

1. Oct 23, 2005

homology

Quick question: what does it mean for a measure to have finite mass? (is this another way of saying sigma finite or something?)

Thanks,

Kevin

2. Oct 24, 2005

mathman

Without context it is hard to say. However, it probably means that the measure of the set in question is finite.

3. Oct 25, 2005

Lonewolf

I wonder if you've come across linear operators called m-currents recently? Is this a question from geometric measure theory?

4. Oct 25, 2005

homology

Not recently, I'm aware of currents and they're on my short list (as is GMT). However, the question over what "they" mean by a measure with finite mass has popped up in a couple places. But here's one:

I'm using Peter Lax's functional analysis text (very nice by the way) and amoung many uses here's one:

Th. 14: Let Q be a compact hausdorff space, C(Q) the space of continuous real-valued functions on Q, normed by the max norm.

(i) C' consists of all signed measures m of finite total mass, defined over all Borel sets. That is, every bounded linear functional L on C(q) can be written as

L(f)=Integral over Q of f dm
and so on and so forth...

5. Oct 25, 2005

Lonewolf

Ok then. What it means is that the measure m has to satisfy |m|(Q) < infinity, where |m| is the total variation of the measure m. That help you any?

6. Oct 26, 2005

homology

Yeah that helps, thanks.

kevin