We consider the framework of Bernoulli measures for heap monoids. We introduce in this framework the notion of asynchronous stopping time, which generalizes 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. We study a sub-additive version of the law of large numbers in this framework.
['Samy Abbes']
A cut-invariant law of large numbers for random heaps