Let (X=[0,1]). Find the (sigma)-algebra generated by the sets (i). (left(0, frac{1}{2}ight)); (ii). (left[0, frac{1}{4}ight),left(frac{3}{4}, 1ight]); (iii).
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Let \(X=[0,1]\). Find the \(\sigma\)-algebra generated by the sets
(i). \(\left(0, \frac{1}{2}ight)\);
(ii). \(\left[0, \frac{1}{4}ight),\left(\frac{3}{4}, 1ight]\);
(iii). \(\left[0, \frac{3}{4}ight],\left[\frac{1}{4}, 1ight]\).
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