  We start with a brief overview of the known facts about the spaces of
discrete Radon measures those may be considered as generalizations of
configuration spaces. Then we study three Markov dynamics on the spaces of
discrete Radon measures: analogues of the contact model, of the
Bolker--Dieckmann--Law--Pacala model, and of the Glauber-type dynamics. We show
how the results obtained previously for the configuration spaces can be
modified for the case of the spaces of discrete Radon measures.
