Help with Wikipedia entry on Lebesgue integration

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Help with Wikipedia entry on Lebesgue integration

Postby selftaught » Wed Nov 20, 2013 12:49 am

Hello

I have a question about http://en.wikipedia.org/wiki/Lebesgue_integration#Intuitive_interpretation , which states:

" Suppose that f : R → R is a non-negative real-valued function. Using the "partitioning the range of f " philosophy, the integral of f should be the sum over t of the area of the thin horizontal strip between y = t and y = t + dt. This area is just mu ( {x: f(x)> t } ) dt "

In keeping with the 'partioning the range; shouldn't this be : 'This area is just mu ( {x: t+ dt > f(x)> t } ) dt '

I know I am wrong as i have seen this here too http://en.wikipedia.org/wiki/Expected_value#General_definition :?:

Thank you
selftaught
 
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Joined: Sun Apr 25, 2010 9:13 pm

Re: Help with Wikipedia entry on Lebesgue integration

Postby selftaught » Wed Nov 20, 2013 7:23 am

Actually i can see this now , please ignore :oops:

I got confused by the reference to horizontal strip between y = t and y = t + dt
selftaught
 
Posts: 21
Joined: Sun Apr 25, 2010 9:13 pm


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