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Let R be a set and (S; B) be a measurable space. Let X : R -> S be a function. Show that the collection of all subsets of R given in f={Inverse of X(A) : A belongs to B} is a sigma algebra.

I can prove for countable union and intersection condition. But not able to solve other conditions for sigma algebra.

Not a homework. Part of book exercise I am trying to solve.

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  • $\begingroup$ Which "other conditions for sigma algebra" do you have problem with? $\endgroup$ – Did Sep 15 '13 at 21:11
  • $\begingroup$ The empty and full set conditions , those I couldn't comprehend. $\endgroup$ – user669083 Sep 15 '13 at 21:43

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