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?