probability through problems by marek capinski
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'I'I\I\ory and Problems
1'" I "", we consider families of sets satisfying conditions similar to I I 11"")',"1 ' 1.1111.11 those imposed on fields. Because computing probability
l it hi I " V":I I,ll<; approximation of events by sequences of simpler ones, we I III I IIll1ll'1! I,hat the union of a sequence of events is always an event.
'''I 111111 Ii.l .A family F of subsets of a non-empty set n is called a /,/ ( 1". 11111 liC'ld) on n if
(I I I , \,\. , " E F , then Uoo Ai E F.
1. = 1
I I, 1111 111.:1 ,,(, I~ rr- fi ·ld are called events.
1111 1II II diliolli H or t.his definition can be read as follows:
1111 f'I "I' 1111 "Jlt.c:OI1lCS is an event.;
I IIIIIP),'III"III, nf' an event is an event;
1111 11111111. "I' II, ~('q1H !lIC:f ! of events is an event.
1111 111111, II tI /i"It! is also 11, liold.
I I I 1, .101 , III lillik, 1,111'11 it i, Ills" H rr- lidd.
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