Probability through problems by marek capinski

'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.