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