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(Solved): Measure Theory Let F:X + Y A Function And BCP(Y). Prove That Af-'(B)) = F -(AB)), Sif-(B)) = F'(S(B) ...

Measure\thinspace Theory\newline Let\thinspace f:X\rightarrow Y\thinspace a\thinspace function\thinspace and\thinspace B\subset \mathbb{P}(Y).\thinspace Prove\thinspace that\newline A(f^{-1}(B))=f^{-1}(A(B)),\thinspace \thinspace S(f^{-1}(B))=f^{-1}(S(B))

Where\thinspace S\thinspace is\thinspace a\thinspace \sigma -algebra\thinspace of\thinspace subsets\thinspace of\thinspace X,\thinspace and\thinspace A\thinspace is\thinspace an\thinspace algebra\thinspace of\thinspace subsets\thinspace of\thinspace X

Measure Theory Let f:X + Y a function and BCP(Y). Prove that Af-'(B)) = f -(AB)), sif-(B)) = f'(S(B))

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