For nonnegative measurable functions,
On , the functionsconverge pointwise to zero but satisfy . Hence the two sides of Fatou lemma can be zero and one.
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Fatou's Lemma is a result in measure theory, particularly in the context of Lebesgue integration. It provides a relationship between limits of integrals and the integral of limits of measurable functions. Specifically, it deals with the behavior of non-negative measurable functions.