Past exam of the information theory course of the University of Oxford / 2023 / 2 / a

The independent and identically distributed hypothesis factors the joint probability mass function:Symbols outside the support of a probability distribution $p$ never occur, almost surely. On its finite positive probability support, $\log p(X_i)$ is bounded, so the strong law of large numbers applies:This is the asymptotic equipartition property with the sign appropriate to a logarithm of a probability mass.