Let (X, A, p) and (Y, B, v) be the measure spaces given X = Y...

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Let (X, A, p) and (Y, B, v) be the measure spaces given X = Y = [0, 1] A = B = B[0,1], the o-algebra of the Borel sets in [0, 1], = μL and v is the counting measure. Consider the product measurable space (X x Y,o(A x B)) and a subset in it defined by E= {(x, y) = XxY: x=y}. Show that (a) EE o(A x B), L. (L, Xedv) dj + L (L xxvdje) de. ‡ x ² XEdu (1) Why is Tonelli's theorem not applicable? Let (X, A, p) and (Y, B, v) be the measure spaces given X = Y = [0, 1] A = B = B[0,1], the o-algebra of the Borel sets in [0, 1], = μL and v is the counting measure. Consider the product measurable space (X x Y,o(A x B)) and a subset in it defined by E= {(x, y) = XxY: x=y}. Show that (a) EE o(A x B), L. (L, Xedv) dj + L (L xxvdje) de. ‡ x ² XEdu (1) Why is Tonelli's theorem not applicable?

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