Let
G be a countable discrete infinite amenable group which acts continuously on a compact metric space
X and let
μ be an ergodic
G-invariant Borel probability measure on
X. For a fixed tempered Følner sequence {
F n } in
G with
\({lim _{n \to + \infty }}\frac{{\left| {{F_n}} \right|}}{{\log n}} = \infty \), we prove the following result:
$$h_{top}^B\left( {{G_\mu },\left\{ {{F_n}} \right\}} \right) = {h_\mu }\left( {X,G} \right),$$
where
G μ is the set of generic points for
μ with respect to {
F n } and
htop B (
G μ ; {
F n }) is the Bowen topological entropy (along {
F n }) on
G μ . This generalizes the classical result of Bowen (1973).