measure-preserving transformation

measure-preserving transformation

[¦mezh·ər pri¦zərv·iŋ ‚tranz·fər′mā·shən]
(mathematics)
A transformation T of a measure space S into itself such that if E is a measurable subset of S then so is T -1 E (the set of points mapped into E by T) and the measure of T -1 E is then equal to that of E.