here is what i wanted to clarify for a long time but could find the answer.

when they say $\displaystyle g$ is a integrable function over a measurable set, it is $\displaystyle \int g < \infty$ or $\displaystyle \int |g| < \infty$? i ve seen the definition that says a nonnegative measurable function $\displaystyle g$ is called integrable if $\displaystyle \int g< \infty$. but when they do not say anything about $\displaystyle g$ being nonnegative but $\displaystyle g$ is integrable, what can be assumed? $\displaystyle \inf g < \infty$ or $\displaystyle \int |g| < \infty$?