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

1. Feb 14, 2009

### lysangc

I am studying 'ANALYSIS by Lieb and Loss '...

usually lebesgue integral is defined in terms of simple function

But

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

$$\int f d\mu : = \int_0^{\infty} \mu (\{x \in X : f(x) > t \}) dt$$
of course, $$\mu$$ 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..