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 $\int |g| < \infty$?
2. f is integrable iff $\int |f| ~ d\mu <\infty$