please give a detailed answer, not just copy from the old chegg answers, really appreciate

3 Suppose (X, S) is a measurable space and f: X + (0,00] is a function. Let B denote the o-algebra of Borel subsets of (0,00). Prove that U, ESB if and only if f is an S-measurable function. 3 Suppose (X, S) is a measurable space and f: X + (0,00] is a function. Let B denote the o-algebra of Borel subsets of (0,00). Prove that U, ESB if and only if f is an S-measurable function