sigma -fieled

[hadiSanji]

Let \(X : \Omega \rightarrow R\) and \(F\) be a class of subsets of \(R\).
show \(\sigma(X^{-1} (F))=X^{-1}(\sigma(F))\) where \(X^{-1} (F)={X^{-1} (A):A\in F}\)

 

[Dason]

http://www.talkstats.com/showthread.php/57-We-only-provide-homework-help-to-those-who-show-effort

And I edited your post a little to make the math look nicer.

 

[BGM]

http://math.stackexchange.com/questions/7881/preimage-of-generated-sigma-algebra

Anyway one key fact should be the preimage operator commute with (countable numbers of) set operators