Let $(S,\mathcal S)$ be a measurable space, let $P$ be a probability measure on $(S,\mathcal S)$, and let $(\Omega,\mathcal A,\mathbb P)$ be a [probability space](/page/Probability%20Space) carrying independent identically distributed random variables $X_1,X_2,\dots:(\Omega,\mathcal A)\to(S,\mathcal S)$ with common distribution $P$. Let $\mathcal F$ and $\mathcal G$ be classes of [measurable functions](/page/Measurable%20Functions) $S\to\mathbb R$, set $\mathcal E:=\mathcal F\cup\mathcal G$, and suppose that $\mathcal E$ is $P$-Donsker in a measurable separable version. Define \begin{align*}\mathcal H:=\mathcal F+\mathcal G:=\{f+g:S\to\mathbb R:f\in\mathcal F,\ g\in\mathcal G\}.\end{align*} Let $\sim$ be the [equivalence relation](/page/Equivalence%20Relation) on $\mathcal F\times\mathcal G$ defined by \begin{align*}(f,g)\sim(f',g')\quad\Longleftrightarrow\quad f+g=f'+g'\quad P\text{-a.s.}\end{align*} and write $Q:=(\mathcal F\times\mathcal G)/\sim$ with quotient map $\pi:\mathcal F\times\mathcal G\to Q$. Equip $Q$ with the canonical Brownian-bridge semimetric \begin{align*}d_Q(\pi(f,g),\pi(f',g')):=\left(P\{(f+g)-(f'+g')\}^2-\left(P\{(f+g)-(f'+g')\}\right)^2\right)^{1/2}.\end{align*} Assume that the empirical process indexed by $\mathcal H$ is represented as the quotient-indexed process on $Q$, that this quotient-indexed version is measurable and separable with respect to $d_Q$, that its pullback through $\pi$ is the decomposition-indexed process $(f,g)\mapsto \sqrt n\{P_n(f+g)-P(f+g)\}$, and that the Brownian-bridge limit on $Q$ is taken in the corresponding measurable separable quotient version. Then $\mathcal H$ is $P$-Donsker.