3
$\begingroup$

According to the book the following is true:

Let $f$ be a measurable function and suppose $|f| \leq h$ where $h$ is a real-valued function and $h$ is integrable. Then f is integrable.

My question is: suppose instead we have the inequality $ |f| \leq h$ but almost everywhere and of course $h$ assumed to be integrable. Is it still true that f is integrable?

Would this follow because the sets of measure zero "don't count" when integrating?

  • 0
    According to *what* book?2010-11-11
  • 1
    @Mariano: **The** book.2010-11-11
  • 0
    @Mariano: Fremlin's book.2010-11-12

1 Answers 1