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Measures with finite mass

  1. Oct 23, 2005 #1
    Quick question: what does it mean for a measure to have finite mass? (is this another way of saying sigma finite or something?)


  2. jcsd
  3. Oct 24, 2005 #2


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    Without context it is hard to say. However, it probably means that the measure of the set in question is finite.
  4. Oct 25, 2005 #3
    I wonder if you've come across linear operators called m-currents recently? Is this a question from geometric measure theory?
  5. Oct 25, 2005 #4
    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...
  6. Oct 25, 2005 #5
    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?
  7. Oct 26, 2005 #6
    Yeah that helps, thanks.

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