Monotonicity of the Lebesgue integral
= Monotonicity of the Lebesgue integral
If measurable functions satisfy $f\leq g$ almost everywhere, then
$$
\int f\,d\mu\leq\int g\,d\mu
$$
whenever the two sides are defined.
= Monotonicity of the Lebesgue integral
If measurable functions satisfy $f\leq g$ almost everywhere, then
$$
\int f\,d\mu\leq\int g\,d\mu
$$
whenever the two sides are defined.