A problem related to the arithmetic of probability measures on the sphere

The class I_o is described in the convolution semigroup of probability measure on the sphere in Rⁿ which are invariant under rotations about a fixed axis; it is established that the indecomposable measures form a dense set in the topology of weak convergence.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 87, pp. 143–158, 1979.I am deeply grateful to Professor I. V. Ostrovskii for the continual attention he has paid to my work.