3
$\begingroup$

I have a really general question. Luzin's theorem implies that Lebesgue measurable functions are continuous almost everywhere. So is there an analogous version of the intermediate value theorem for measurable functions, with maybe some extra conditions?

Thanks!

  • 0
    Since the heavyside function is measurable, what kind of analogouous statement do you expect?2012-10-08
  • 1
    You have a good point, but I was wondering if it was possible to add some stronger hypothesis on measurable functions to get the intermediate value theorem, without necessarily asking the function to be continuous.2012-10-08

1 Answers 1