What is a Measure with Finite Mass?

[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

 

[mathman]

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

 

[Lonewolf]

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

 

[homology]

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

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...

 

[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?

 

[homology]

Yeah that helps, thanks.

kevin