The set formula_2 is understood to be the total space to be filled: the mixing bowl, the smoke-filled room, "etc." The measure formula_3 is understood to define the natural volume of the space formula_2 and of its subspaces. The collection of subspaces is denoted by formula_5, and the size of any given subset formula_6 is formula_7; the size is its volume. Naively, one could imagine formula_5 to be the power set of formula_2; this doesn't quite work, as not all subsets of a space have a volume (famously, the Banach-Tarski paradox). Thus, conventionally, formula_5 consists of the measurable subsets—the subsets that do have a volume. It is always taken to be a Borel set—the collection of subsets that can be constructed by taking intersections, unions and set complements; these can always be taken to be measurable.