What is Reddit's opinion of Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance)?

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I think this question is a great example of why probability theory requires so much measure theory.

The probability of the finite sequence (H,H,H, ..., H) approaches zero as you increase the size of the sequence to infinity. The probability that the sequence does not occur is said to be "Almost Surely".

But this statement holds for any sequence you write down. Any specific sequence of heads and tails does not occur with probability "Almost surely".

Yet the space of possible outcomes is a probability space, so we require the sum of probabilities of all outcomes to be: Prob({space of all outcomes}) = 1.

This has implications on the construction of the probability space associated with these "experiments" of infinite coin tosses. This is very related to measure theory, where the set [0,1] has the same measure (length) as the set (0,1).

The book Shreve - Stochastic Calculus for Finance II: Continuous-Time Models happens to start off with precisely this example to explain the idea of a probability space, without going too deep into measure theory and all that.