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

Question about integrable functions

  1. Apr 8, 2010 #1
    Suppose you have a nonnegative Lebesgue measurable function supported on [tex][0,1][/tex] such that [tex]\int_0^1 f = \infty[/tex]. Does this mean that the set [tex]E = \{ x\in [0,1] : f(x) = \infty \}[/tex] has positive Lebesgue measure?
  2. jcsd
  3. Apr 8, 2010 #2
    No. Consider the function [itex]f\left(x\right)=1/x[/itex], and whatever value you want at x = 0.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook