  In this note we prove the Banach space properties of the homogeneous
Newton-Sobolev spaces $HN^{1,p}(X)$ of functions on an unbounded metric measure
space $X$ equipped with a doubling measure supporting a $p$-Poincar\'e
inequality, and show that when $1<p<\infty$, even with the lack of global
$L^p$-integrability of functions in $HN^{1,p}(X)$, we have that every bounded
sequence in $HN^{1,p}(X)$ has a strongly convergent convex-combination
subsequence. The analogous properties for the inhomogeneous Newton-Sobolev
classes $N^{1,p}(X)$ are proven elsewhere in existing literature
