The above is enough to build up a measure-preserving dynamical system, in its entirety. The sets of formula_49 or formula_51 occurring in the formula_32'th place are called cylinder sets. The set of all possible intersections, unions and complements of the cylinder sets then form the Borel set formula_5 defined above. In formal terms, the cylinder sets form the base for a topology on the space formula_2 of all possible infinite-length coin-flips. The measure formula_3 has all of the common-sense properties one might hope for: the measure of a cylinder set with formula_49 in the formula_57'th position, and formula_51 in the formula_59'th position is obviously 1/4, and so on. These common-sense properties persist for set-complement and set-union: everything except for formula_49 and formula_51 in locations formula_57 and formula_59 obviously has the volume of 3/4. All together, these form the axioms of a sigma-additive measure; measure-preserving dynamical systems always use sigma-additive measures. For coin flips, this measure is called the Bernoulli measure.