  The main problem in the area of graph property testing is to understand which
graph properties are \emph{testable}, which means that with constantly many
queries to any input graph $G$, a tester can decide with good probability
whether $G$ satisfies the property, or is far from satisfying the property.
Testable properties are well understood in the dense model and in the bounded
degree model, but little is known in sparse graph classes when graphs are
allowed to have unbounded degree. This is the setting of the \emph{sparse
model}.
  We prove that for any proper minor-closed class $\mathcal{G}$, any monotone
property (i.e., any property that is closed under taking subgraphs) is testable
for graphs from $\mathcal{G}$ in the sparse model. This extends a result of
Czumaj and Sohler (FOCS'19), who proved it for monotone properties with
finitely many forbidden subgraphs. Our result implies for instance that for any
integers $k$ and $t$, $k$-colorability of $K_t$-minor free graphs is testable
in the sparse model.
  Elek recently proved that monotone properties of bounded degree graphs from
minor-closed classes that are closed under disjoint union can be verified by an
approximate proof labeling scheme in constant time. We show again that the
assumption of bounded degree can be omitted in his result.
