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let f be a nonnegative measurable function. then there is a sequence <pi n> of simple functiion with pi n+1>=pi n, such that f = lim pi n at each point of x. if f is defined on a sigma finite measure space. we may choose the function pi n so that each vanishes outside a set of a finite measure.
Suppose that ( X,M,U) is measurable space , f and each fn are integrable and non-negative , fn maps to f a.e , and integration of fndu maps to integration of fdu. Prove that for each A is element of U. Integration of fndu maps to integration of fdu.
lim 𝑥→0+ (sin 𝑥) ^x
From a piece of wire 30 cm long, it is required to bend a rectangle of the largest area. What are the dimensions of this rectangle
2n/3^(n+1) where n is from 1 to infinity
f(x) = cos x - sin x has an extreme value in the interval (-Ã /2,Ã /2).
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