Fatou’s identity and Lebesgue’s convergence theorem

Klei, Heinz-Albrecht

doi:10.1090/S0002-9939-99-05099-6

Fatou’s identity and Lebesgue’s convergence theorem
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by Heinz-Albrecht Klei

Proc. Amer. Math. Soc. 127 (1999), 2297-2302

DOI: https://doi.org/10.1090/S0002-9939-99-05099-6

Published electronically: April 9, 1999

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Abstract:

The classical Fatou lemma for bounded sequences of nonnegative integrable functions is represented as an equality. A similar result is stated for measure convergent sequences. Neither result requires a uniform integrability assumption. For the latter a converse is proven. Two extensions of Lebesgue’s convergence theorem are presented.

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