Towards convolutions on configuration spaces

We study convolutions of probability measures on configuration spaces as well as convolutions of functions on the spaces of finite configurations. We describe connections between the convolution of measures and the Ruelle convolution of their correlation functions. We present simple conditions when the Ruelle convolution of the correlation functions of the probability measures will be a correlation function also. We study derivative operators with respect to Ruelle convolution and we show how to use properties of a such operator for the describing properties of the stochastic contact model in continuum. We consider question about the convolution of the Gibbs measures also. Additional information and comments: This is update of the previous ukrainian version for the my registration information.