Probabilistic Ideas and Methods in Analytic Number Theory (part I?)

In these notes, Section 2 consists of the number-theoretic discussion, whereas Section 3 provides the probabilistic background (with relatively few proofs). First we draw upon topology and group theory to give some examples of probability spaces. Perhaps the most interesting is the weighted Bernoulli space Bp which models flipping a – fixed but not necessarily fair – coin infinitely many times. In the sequel, we develop sufficient background to state Chebyshev’s Inequality, the Law of Large Numbers, the Central Limit Theorem, and the Khinchin-Kolmogorov Law of the Iterated Logarithm.