Knowing an event obtains with probability one is interchangeable with absolute certainty
In probability theory, an event having a probability of one means it occurs 'almost surely,' which is distinct from absolute certainty when dealing with infinite sample spaces where zero-probability events can still occur.
Judged against reference works: claims of this kind are settled by reference works, not journal abstracts.
math.stackexchange.com: How likely/unlikely is an event with probability $1$/$0$?. math.stackexchange.com. https://math.stackexchange.com/questions/1446351/how-likely-unlikely-is-an-event-with-probability-1-0
Notes that an event with probability zero can still happen, contradicting interchangeability.
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math.stackexchange.com: What's the difference between almost surely and surely?. math.stackexchange.com. https://math.stackexchange.com/questions/2900416/whats-the-difference-between-almost-surely-and-surely
Explains the difference between 'surely' and 'almost surely' in infinite sample spaces.
en.wikipedia.org: Almost surely. en.wikipedia.org. https://en.wikipedia.org/wiki/almost_surely
Shows that an event of probability 1 can leave open non-empty sets, separating 'surely' from 'almost surely'.
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