= Solution
The <conditional class probability> is $p_k(x)=\mathbb P(Y=k\mid X=x)$. A <Bayes classifier> chooses
$$
h^*(x)\in\operatorname*{argmax}_{1\leq k\leq K}p_k(x),
$$
and its <Bayes risk> is
$$
R_{\mathrm{Bayes}}=R(h^*)
=\mathbb E\left[1-\max_kp_k(X)\right].
$$
A sequence of classifiers is <risk consistency>[consistent] when $R(h_n)\to R_{\mathrm{Bayes}}$ as $n\to\infty$, with convergence interpreted in probability or in expectation according to whether the training sample is conditioned upon.
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