In any finite group G, the commutativity degree of G (denoted by d(G)) is the probability that two randomly chosen elements of G commute. More generally, for every n \geq 2 the multiple commutativity degree (denoted by d_n(G)) is the probability that a randomly chosen ordered (n+1)-tuple of the group elements is mutually commuting. In this paper we will generalize the definition of multiple commutativity degree to every compact group G (infinite and even uncountable).
