= Solution
The <geometric drift condition> requires a measurable $V:\mathcal X\to[1,\infty)$, a <small set> $C$, constants $\lambda\in(0,1)$ and $b<\infty$, and
$$
\boxed{PV(x)\leq\lambda V(x)+b\mathbf1_C(x)\qquad(x\in\mathcal X).}
$$
Smallness means that for some $m\geq1$, $\varepsilon>0$, and <probability measure> $\nu$, $P^m(x,\cdot)\geq\varepsilon\nu(\cdot)$ for every $x\in C$. With irreducibility and aperiodicity, this <drift-minorisation condition> implies <geometric ergodicity>. The function $V$ controls the chain away from the small set; inside that set the additive constant allows unrestricted bounded drift.
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