  We extend the geometric side of Arthur's non-invariant trace formula for a
reductive group $G$ defined over $\mathbb{Q}$ continuously to a natural space
$\mathcal{C}(G(\mathbb{A}^1))$ of test functions which are not necessarily
compactly supported. The analogous result for the spectral side was obtained in
[MR2811597]. The geometric side is decomposed according to the following
equivalence relation on $G(\mathbb{Q})$: $\gamma_1\sim\gamma_2$ if $\gamma_1$
and $\gamma_2$ are conjugate in $G(\bar{\mathbb{Q}})$ and their semisimple
parts are conjugate in $G(\mathbb{Q})$. All terms in the resulting
decomposition are continuous linear forms on the space
$\mathcal{C}(G(\mathbb{A})^1)$, and can be approximated (with continuous error
terms) by naively truncated integrals.
