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We begin by listing some standard definitions in the theory of probability. A probability space is a set Ω of elements ω together with a σ-field m of subsets of Ω on which is defined a completely additive measure P such that P(Ω) = 1. A real-valued P-meastirable function X = X (ω) is a random variable, and the function \(F\left( x \right) = P\left\{ {X \leqslant x} \right\}\) where {} denotes the set of all ω to such that the relation within the braces holds, is the distribution function of X. The sets of a sequence A1,A2,… are independent if for every finite set i1,…, in of distinct integers, \(P\left( {\mathop \prod \limits_{r = 1}^n {A_{{i_r}}}} \right) = \mathop \prod \limits_{r = 1}^n P({A_{{i_r}}})\),and the random variables of a sequence X1, X2 ... are independent if, for every sequence x1, x2, … of real numbers, the sets \(\left\{ {{X_1} \leqslant {x_1}} \right\},\left\{ {{X_2} \leqslant {x_2}} \right\}\), … are independent.
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