This article considers the relation between total factor productivity measures for individual production units and those for aggregates such as industries, sectors or economies. This topic has been treated in a number of influential publications, such as Hulten (1978), Gollop (1979) and Jorgenson et al. (1987). What distinguishes this article from other publications in this area is that I deliberately avoid the making of all kinds of (neoclassical) structural and behavioural assumptions, such as the existence of production frontiers with certain properties, or optimizing behaviour of the production units. In addition, I also treat dynamic ensembles of production units, characterized by entry and exit. Thus, a greater level of generality is achieved from which the earlier results follow as special cases.