1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Real Analysis: Are lebesgue measures metrics?

  1. Oct 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Are Lebesgue measures considered metrics?

    3. The attempt at a solution
    I have an elementary understanding of metrics and am currently learning about Lebesgue Integration. A Lebesgue measure as a length in Euclidean space should be a metric, but what about areas and volumes? I'm thinking no because metrics are distances, which to me means length. Is there a way I can prove this? Are there necessary properties of each that agree or disagree?
     
  2. jcsd
  3. Oct 23, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    A "metric" is a way of measuring the size of a set, not just the "length" of an interval. We use "metrics" in 2 and 3 dimensions all the time!
     
  4. Oct 23, 2008 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    No. Because, as you said, a metric measures the distance between two things. A 'measure' (in the Lebesgue measure sense) measures the size of one thing. How can one be the other? The number of 'things' is different.
     
  5. Oct 23, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Oh, I see your point. Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Real Analysis: Are lebesgue measures metrics?
Loading...