  Heap monoids equipped with Bernoulli measures are a model of probabilistic
asynchronous systems. We introduce in this framework the notion of asynchronous
stopping time, which is analogous to the notion of stopping time for classical
probabilistic processes. A Strong Bernoulli property is proved. A notion of
cut-invariance is formulated for convergent ergodic means. Then a version of
the Strong law of large numbers is proved for heap monoids with Bernoulli
measures. Finally, we study a sub-additive version of the Law of large numbers
in this framework based on Kingman sub-additive Ergodic Theorem.
