- #1
lysangc
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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 !
[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!
-------------------------------
P.S. Sorry for poor english..
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!
-------------------------------
P.S. Sorry for poor english..