Question: Let (W, A , P ) = ((0, 1), B(0, 1), l), where l is the Lebesgue measure, and let X n be a r.v.

Let (W,A,P) = ((0, 1), B(0, 1), l), where l is the Lebesgue measure, and letXnbe a r.v. defined by

1, ωε 0, Π n = 1, 2, .. Ξ Xn = 0, ωε

Then show that

Let ((, A, P) = ((0, 1), B(0, 1), (),

For any r > 0, and

Let ((, A, P) = ((0, 1), B(0, 1), (),

Indeed,

Let ((, A, P) = ((0, 1), B(0, 1), (),

Pointwise.

1, 0, n = 1, 2, .. Xn = 0,

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