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+ Если $A in cal(A) => overline(A) in cal(A)$
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+ Если $A, B in cal(A) => A union B in cal(A)$
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- *$sigma$-алгеброй* назовём класс подмножеств $cal(F)$ такой, что
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- + $Omega in cal(F)$
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- + Если $A in cal(F)$, то $overline(A) in cal(F)$
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- + Если ${A_i}_(i=1)^infinity in cal(F)$, то $limits(union.big)^infinity_(i=1) A_i in cal(F)$
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-
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*$sigma$-алгеброй событий* называется множество $cal(F)$ подмножеств $A subset Omega$, удовлетворяющее условиям:
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A1) $Omega in cal(F)$\
@@ -206,7 +201,7 @@ $ P(A| A_i) gt.eq 0 $
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Тогда
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- $ P(A) = limits(sum)_(i = 1)^infinity P(A_i) dot P(A \\ A_i) $
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+ $ P(A) = limits(sum)_(i = 1)^infinity P(A_i) dot P(A | A_i) $
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Доказательство:
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