Question: 1. Let = [0, 1). For , we define n, n N in terms of the binary expansion = X n n 2 n We

1. Let = [0, 1). For , we define n, n N in terms of the binary expansion = X n n 2 n We define events An = { : n = 0} n and C = { : is irrationnal}. (a) Express events C in terms of events An.

(b) Is event C in the asymptotique sigma algebra of (An)nN?

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