Discuss about a measurable function
Discuss the below:
Q: Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x.
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Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x.
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Consider the functions f(x) = x^2 and g(x) = square root of x, both with domain and co-domain R+, the set of positive real numbers.
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