sigma -fieled

**hadiSanji** · 12-16-2011 11:47 AM

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** · 12-16-2011 11:54 AM

http://www.talkstats.com/showthread....ho-show-effort

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

**BGM** · 12-16-2011 12:25 PM

http://math.stackexchange.com/questi...-sigma-algebra

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

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