6.6 Limit theorems of probability

The main goal of this section is to give a constructive proof of Theorem 6.1, which says that event (6.1) holds strictly almost surely. The simple proof given here is inspired by [412] (proof of Theorem 3.1).

We say that a non-negative supermartingale c06-math-0576 forces an event c06-math-0577 if c06-math-0578 for every c06-math-0579 not in c06-math-0580. We are required to construct a supermartingale forcing (6.1), where we can set c06-math-0581, as we mentioned in Section 6.2. This is not difficult given Theorem 6.2.

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