Hello Could you plese help me on this exercise? Let F1 and F2 two sigma algebras of subsets of and Prove that is a sigma algebra.
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Apply the definition. Show that : (i) ; (ii) If , show that ; (iii) Let . Show that .
Another way: which by hypothesis is -algebra.
We notice that the hypothesis (or ) is necessary: if we consider , and then which is not a -algebra since .
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