  Given a general Anosov $\mathbb{R}^\kappa$ action on a closed manifold, we
study properties of certain invariant measures that have recently been
introduced in \cite{BGHW20} using the theory of Ruelle-Taylor resonances. We
show that these measures share many properties of Sinai-Ruelle-Bowen measures
for general Anosov flows such as smooth disintegrations along the unstable
foliation, positive Lebesgue measure basins of attraction and a Bowen formula
in terms of periodic orbits. Finally we show that if the action in the positive
Weyl chamber is transitive, the measure is unique and has full support.
