Determine whether each of the following statements is true or false and justify your answer. (a) Let X be a nonempty set. If (X, A, µ) is a measure space and f : X R is a function, then F = {f(E): E € A} is a o-algebra on R. (b) Let X be a nonempty set. If (R, M, m) is the Lebesgue measure space and f:X R is a function, then A = {f"(E) : E E M} is a o-algebra on X.

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A: τ={ϕ}∪{U⊂X :Uc is finite }  (a) Xc=ϕ, which is finite . so X∈τ let A,B∈τ Then Ac,Bcare finite…

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A: Let (X,d) be a metric space to show that {x} is closed sunset of X.

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A: (a) Given that T=x,y,z, L=∅,x,x,y,T is a σ-algebra over T. Since every sigma algebra is measurable.…

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A: Given

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A: we have to solve given problem:

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A: We will show it by giving example

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