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Does someone of you have learned Lebesgue integration in this way? Is it equivalent to a study based directly on Measure Theory? Do I am losing something relevant?

Thanks for opinions and excuse the mediocre english.

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- Thread starter Castilla
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- #1

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Does someone of you have learned Lebesgue integration in this way? Is it equivalent to a study based directly on Measure Theory? Do I am losing something relevant?

Thanks for opinions and excuse the mediocre english.

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mathwonk

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others include the great Functional Analysis, by Riesz and Nagy, and the fine Analysis II by Lang.

There is a simple interplay between sets and functions ni which a set is mirrored by its characteristic function, the fu ntion whiuch equals 1 on the set and 0 off it. The set is measurable iff the function is measurable.

thus approximating functions by step functions is like aproximating sets by rectangles.

one can begin by defining integrals of step functionsm and taking limits of step functions nd studying when the limits of step functions have integrals, or one can begin by studying sets which are limits of rectangles and when etc etc.....

if you have measure theory first then the integral of a positive fucnion can be defined as the measure of the region under the rgaph, and if you have integration first then the measure of a set is the integral of its characteristic function.

comme ci comme ca.

I am not an expert however, indeed a rookie (an old rookie) of sorts in this area.

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