Universal Donsker classes and bounded variation I just read in a paper A Donsker Theorem for Lévy Measures the following statement 

$BV$-balls are universal Donsker classes (page 7, Examples 3.2 - Compound Poisson Processes)

$BV$ stands here for bounded variation.
Unfortunately there is no reference for this result. I was wondering, is this some sort of trivial? Does anyone know a reference?
 A: I found a reference for this statement, by Donsker himself published in 
Dudley,R.M. (1992) "Frechet Differentiability,  p-Variation  and Uniform  Donsker Classes", "The Annals of Probability" (p. 1971)
Theorem (Bounded Variation and universal $P-$Donsker classes):
For any (bounded and unbounded) interval $J\subseteq \mathbb R$, any $p$ with $0<p<2$ and any $M<\infty$, the set of functions $\mathcal{F}_{p,M}$ defined as
$$
 \mathcal{F}_{p,M}:=\{f:\,J\to\mathbb R, v(f,p)\leq M\}
$$
with 
$$
 v(f,p):=v(f,p,J):=\sup\{\sum_{i=1}^n \lvert f(x_i)-f(x_{i-1})\rvert^p:x_0<x_1<\ldots<x_n\in J,n\in\mathbb N \}
$$
is a uniform $P-$Donsker class.
If we choose $p=1$, we have exactly the total variation statement. 
For reference,  in the specific case of the question this then reduces to show that the functions in the class
$$
\mathcal G_{\varphi}:=\Big\{\mathcal F^{-1}\left[\frac{1}{\varphi(-\bullet)}\right] \ast 1_{(-\infty,t]}:\;\lvert t\rvert\geq\zeta>0\Big\}
$$
are of bounded variation, which is true, since in the setting of the question the operator $\mathcal F^{-1}\left[\frac{1}{\varphi(-\bullet)}\right]$ (in the paper called deconvolution operator) is a finite signed measure.
