SUMMARYIn order to study objects forming a sub‐setAof euclidean space, mathematical morphology uses structuring figuresBand notes the frequency of events such as ‘BhitsA’, ‘Bis included intoA’etc. Thus, a probabilistic formalism is associated with this experimental technique and facilitates its interpretation. IfAis considered as a closed set, we obtain a random closed‐sets theory, closely connected with integral geometry. The functionalsTdefined byT(K) =P(A∩K≠ Ø) forKcompact are characterized as alternating capacities of infinite order. Interesting classes of functionalsTare obtained ifAis indefinitely divisible or semi‐markovian. At last, the mathematical notion of granulometry (size distribution) is studied by using a