Proposition 1.1 Suppose that X1, X2,... are random variables. The followingquantities are random variables:(a) max{X1, X2) and min(X1, X2);(b) sup, Xn and inf, Xn;(c) lim sup∞ Xand lim inf∞ Xn-(d) If Xn(w) converges for (almost) every w as n→ ∞, then lim-random variable.→ Xn is a

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Linear Algebra: A Modern Introduction

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Proposition 1.1 Suppose that X1, X2,... are random variables. The following quantities are random variables: (a) max{X1, X2) and min(X1, X2); (b) sup, Xn and inf, Xn; (c) lim sup∞ X and lim inf∞ Xn- (d) If Xn(w) converges for (almost) every w as n→ ∞, then lim- random variable. → Xn is a