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• W2143465876 abstract "The great theorem on convergence of integrals is due in its usual form to Lebesgue [2] though its origins go back to Arzela [1]. It says that the integral of the limit of a sequence of functions is the limit of the integrals if the sequence is dominated by an integrable function. This paper investigates the converse problem — if we know that we may take limits under the integral sign, then what can we say about the convergence? The answer is found for functions of a real variable, but it is easily extended to any space with a countably additive measure. Finally the result is illustrated by an application to Fourier series." @default.
• W2143465876 created "2016-06-24" @default.
• W2143465876 creator A5081741226 @default.
• W2143465876 date "1961-10-01" @default.
• W2143465876 modified "2023-10-10" @default.
• W2143465876 title "On dominated convergence" @default.
• W2143465876 cites W1734053220 @default.
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• W2143465876 doi "https://doi.org/10.1017/s1446788700026598" @default.
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