Question: 4. Consider the following function f : R > IR f = -3 ' 1[2,1] + 2 ' 1[3,+oo) Here 1,; denotes the indicator function

4. Consider the following function f : R > IR f = -3 ' 1[2,1] + 2 ' 1[3,+oo) Here 1,; denotes the indicator function of set A. (a) Evaluate the integral In fat), with respect to the Lebesgue measure A, if it exists. Does function f belong to the P(IR, A) space for some p 2 1? (b) Evaluate the integral In fdl, with respect to the Dirac delta measure concentrated at 1, if it exists. Does function f belong to the '(R, 61) space for some p 2 1

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