= Doob exposure martingale
{c}
{title2=$M_i=\mathbb E[f\mid Z_1,\ldots,Z_i]$}
= Doob martingale of independent coordinates
{c}
{synonym}
Expose independent coordinates successively and take the conditional mean of a function after each exposure. These conditional means form a <martingale> from $\mathbb Ef$ to $f$. A coordinate oscillation bound $c_i$ gives a conditional interval of length $c_i$ for the corresponding increment, by coupling the unexposed coordinates. Applying the <Hoeffding lemma> to these conditional ranges proves the <McDiarmid inequality>.
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