$A$. These definitions obviously extend to an arbitrary measure class preserving action $G{\circlearrowleft}(X,m)$ of a general countable group $G$ on a probability space $(X,m)$. The opposite notions are those of *dissipativity* and of a *wandering set*, i.e., such a set $A$ that all its translates $gA,\,g\in
G,$ are pairwise disjoint. An action is called *dissipative* if it admits a positive measure wandering set, and it is called *completely dissipative* if, moreover, there is a wandering set such that the union of its translates is (mod 0) the whole action space.

Our approach to these properties is based on the observation that the notions of conservativity and dissipativity admit a very natural interpretation in terms of the *ergodic decomposition* of the action (under the assumption that such a decomposition exists, i.e., the action space is a *Lebesgue measure space*). Let ${\mathcal C}\subset X$ denote the union of all the purely non-atomic components, and let ${\mathcal D}=X\setminus{\mathcal C}$ be the union of all the purely atomic ergodic components. We call ${\mathcal C}$ and ${\mathcal D}$ the *continual* and *discontinual* parts of the action, respectively. Further, let ${\mathcal D}_{\mathsf{free}}$ be the subset of ${\mathcal D}$ consisting of the points with trivial stabilizers, i.e., 