  Gao, Jackson, and Seward (see arXiv:1201.0513) proved that every countably
infinite group $\Gamma$ admits a nonempty free subshift $X \subseteq
\{0,1\}^\Gamma$. Furthermore, a theorem of Seward and Tucker-Drob (see
arXiv:1402.4184) implies that every countably infinite group $\Gamma$ admits a
free subshift $X \subseteq \{0,1\}^\Gamma$ that supports an invariant
probability measure. Aubrun, Barbieri, and Thomass\'{e} (see arXiv:1507.03369)
used the Lov\'{a}sz Local Lemma to give a short alternative proof of the
Gao--Jackson--Seward theorem. Recently, Elek (see arXiv:1702.01631) followed
another approach involving the Lov\'{a}sz Local Lemma to obtain a different
proof of the existence of free subshifts with invariant probability measures
for finitely generated sofic groups. Using the measurable version of the
Lov\'{a}sz Local Lemma for shift actions established by the author (see
arXiv:1604.07349), we give a short alternative proof of the existence of such
subshifts for arbitrary groups. Moreover, we can find such subshifts in any
nonempty invariant open set.
