Let be a non-negative Measurable Function. Let be a sequence of such functions. Suppose that . Then also the Integrals . Proof Need to check all cases but simple enough for each Case 1 and Case 2 simple function, Case 3 simple function, simple function Case 4 simple function, Measurable Function Case 5 Measurable Function, Measurable Function, both Proposition Let be a sequence of nonnegative Measurable Functions. Then: