Consider now the special case of maps formula_13 which preserve intersections, unions and complements (so that it is a map of Borel sets) and also sends formula_2 to formula_2 (because we want it to be conservative). Every such conservative, Borel-preserving map can be specified by some surjective map formula_18 by writing formula_19. Of course, one could also define formula_20, but this is not enough to specify all such possible maps formula_13. That is, conservative, Borel-preserving maps formula_13 cannot, in general, be written in the form formula_23 Obviously! one might say; consider, for example, the map of the unit interval formula_24 given by formula_25 this is the Bernoulli map.