I am studying 'ANALYSIS by Lieb and Loss '...(adsbygoogle = window.adsbygoogle || []).push({});

usually lebesgue integral is defined in terms of simple function

But

In this book, integral is defined in terms of Riemann Integration !!!

[tex]\int f d\mu : = \int_0^{\infty} \mu (\{x \in X : f(x) > t \}) dt[/tex]

of course, [tex]\mu[/tex] is measure, f is measurable, non-negative

LHS -> general (lebesgue) integration

RHS -> (improper) Riemann integration

Have you ever seen this definition in any other books?

If so, which book ? I need Reference .. HELP ME PLEASE!!

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P.S. Sorry for poor english..

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# Diffrent definition of Lebesgue integral! Have you ever seen this?

Can you offer guidance or do you also need help?

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