Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lebesgue Outer Measure

  1. Nov 4, 2006 #1
    It is a fact that Lebesgue measure is characterised uniquely by the five requirements:

    1 - measure of empty set = 0
    2 - monotonicity
    3 - measure = length for intervals
    4 - translation invariance
    5 - countable additivity

    It is also true that Lebesgue outer measure satisfies:

    1 - measure of empty set = 0
    2 - monotonicity
    3 - measure = length for intervals
    4 - translation invariance
    5 - countable subadditivity

    but I'm dying to know whether these requirements actually characterise Lebesgue outer measure uniquely.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Lebesgue Outer Measure
  1. Lebesgue measure (Replies: 6)

  2. Lebesgue outer measure (Replies: 1)

Loading...