  While routinely used in other areas of dynamics, image sets are ill-defined
objects in general non-invertible measurable dynamics. We propose a way of
consistently working with image sets of null-preserving (and hence, in
particular, of measure-preserving) maps. This concept is illustrated in the
context of basic ergodic properties like recurrence, ergodicity, exactness and
existence of generators. It allows us to turn various suasive but logically
false statements about set-theoretic images into actual theorems, and to
eliminate extra assumptions on the measurability of images from some classical
results.
