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WannaBe22
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Homework Statement
Let [tex]A \subseteq R [/tex] be a Lebesgue-Measurable set. Prove that if the Lebesgue measure of A is less than infinity , then the function [tex] f(x) = \lambda(A \cap (-\infty,x)) [/tex] is continous.
Homework Equations
The Attempt at a Solution
I'm really confused about the definition of [tex] \lambda (A) [/tex] where [tex] \lambda [/tex] is the Lebesgue-measure...I've tried taking an [tex] \epsilon >0 [/tex] and choosing some [tex] \delta >0 [/tex] for which if [tex] |x-x_0 | < \delta [/tex] then [tex]|f(x)-f(x_0)| <\epsilon [/tex] but I don't think this is the point...
I'll be delighted to get some guidance
Thanks !