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- W2347635343 abstract "This note is devoted to describe the classical Lebesgue integration from a functional point of view.Let C[0,1]be the linear space of all real-valued continuous functions endowed with the norm ||x|| =∫_0~-|x(t)|dt and let X≡C[0,1]be its completion.We define a linear functional x_R~* on C[0,1]by x_R~*,x =∫_K x(t)dt in Riemann's sense,and let x~* be the natural extension of x_R~* from C[0,1]to its completion C[0,1].With a sketch but self-contained proof,we show the Lebesgue integration is just the natural extension of x_R~* to C[0,1],that is,C[0,1]= L_1[0,1]and x~*,x =∫_0~- x(t)dt in Lebesgue's sence." @default.
- W2347635343 created "2016-06-24" @default.
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- W2347635343 date "2011-01-01" @default.
- W2347635343 modified "2023-09-23" @default.
- W2347635343 title "A Functional View of Lebesgue Integration" @default.
- W2347635343 hasPublicationYear "2011" @default.
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