ボレル集合
Every Borel set can, non-uniquely, be built up, starting from intervals with rational endpoints and applying the operations of complement and countable unions, a countable number of times. The record of such a construction is called a "Borel code". Given a Borel set formula_469 in formula_215, one recovers a Borel code, and then applies the same construction sequence in formula_479, getting a Borel set formula_480. It can be proven that one gets the same set independent of the construction of formula_481, and that basic properties are preserved. For example, if formula_482, then formula_483. If formula_469 has measure zero, then formula_480 has measure zero. This mapping formula_486 is injective.