ABSTRACT
Gelfand and Guichardct started the problem of the multiplicative integral (sec, e.g., [13]) which is at the present time still only partially solved, and can be formulated as follows: a positive measure J.L with support X and a Lie group G being given, what arc the multiplicative G-intcgrals \Vhich are multiplicative integrals with respect to J.L? This problem is a particular case of the following one: an clement T of'2b'(X, IR) with support X being given, what arc the multiplicative G-distributions with respect to T?
