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

Signed measures and uniform integrability

  1. Nov 4, 2004 #1


    User Avatar


    If u is a positive measure, I need to show that any finite subset of L^1(u) is uniformly integrable, and if {fn} is a sequence in L^1(u) that converges in the L^1 metric to f in L^1(u), then {fn} is uniformly integrable.

    I know that a collection of functions {f_alpha}_alpha_in_A subset L^1(u) is uniformly integrable if for every e > 0 there exists a d > 0 such that |int_E f_alpha du| < epsilon for all alpha in A whenever u(E) < delta, but I am stuck on the proofs. Any assistance is appreciated, thanks.
  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: Signed measures and uniform integrability