Currently I am enrolled in the course of Advanced Probability Theory. I never studied topology before and for the first time I am studying measurable function in this course. I understand what we mean by Measurable function. Definition of Measurable fuction goes as follows:
Let A and B be sigma-algebra defiend on spaces X and Y, respectively. So, (X, A) and (Y, B) are measurable spaces. A map f:X->Y is measurable if for all b (that belongs to B), there is an inverse image in A.
Immediately after this defintion, they explain Borel Measurable and Lebesgue measurable fucntion. They have explained in terms of Topological space. Since I am unaware about Topology I cannot grab the definition of Borel Measurable and Lebesgue measurable fucntion. Can you please explain me in simple notations avoiding the context of Topology. Hope it is possible explaining in that way.
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