# Lebesgue integral

• Dec 22nd 2009, 04:54 PM
GTO
Lebesgue integral
here is what i wanted to clarify for a long time but could find the answer.
when they say $g$ is a integrable function over a measurable set, it is $\int g < \infty$ or $\int |g| < \infty$? i ve seen the definition that says a nonnegative measurable function $g$ is called integrable if $\int g< \infty$. but when they do not say anything about $g$ being nonnegative but $g$ is integrable, what can be assumed? $\inf g < \infty$ or $\int |g| < \infty$?
• Dec 23rd 2009, 12:12 AM
Moo
f is integrable iff $\int |f| ~ d\mu <\infty$ :)