This exercise shows that an arbitrary sequence of events in a sample space can be written as

Question:

This exercise shows that an arbitrary sequence of events in a sample space can be written as the union of increasing events. Let {An}n≥1 be a sequence of events in a sample space (not necessarily monotone), and define a new sequence {Cn}n≥1 by Cn = ∪n i=1Ai, n = 1, 2,….

(i) Show that {Cn}n≥1 is an increasing sequence of events in Ω.

(ii) Verify that image text in transcribed