= Solution
The <tail sigma-algebra> is
$$
\boxed{\mathcal T=\bigcap_{N\geq1}\sigma(X_N,X_{N+1},\ldots).}
$$
Its <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:
$$
\boxed{A\in\mathcal T\ \Longrightarrow\ \mathbb P(A)\in\{0,1\}.}
$$
Identical <probability distributions> and <integrable random variable>[integrability] are not required for the <Kolmogorov zero-one law>.
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