I'm trying to think of an example of a probability space (Ω,β,p) such that Ω is an infinite sample space but |β| < ∞, or to prove that no such a probability space can exist.
Thank you
2026-03-29 21:20:17.1774819217
Infinite sample space of Ω
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Take Ω any infinite set and β = {Ω,∅}, with p(Ω) = 1 and p(∅) = 0.