Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 201 / 3 / a / Solution

The tail sigma-algebra isIts events depend only on arbitrarily late coordinates. The Kolmogorov zero-one law states that for a sequence of independent random variables, every tail event has probability zero or one:Identical probability distributions and integrability are not required for the Kolmogorov zero-one law.