invariant measure


invariant measure

[in′ver·ē·ənt ′mezh·ər] (mathematics) A Borel measure m on a topological space X is invariant for a transformation group (G,X,π) if for all Borel sets A in X and all elements g in G, m (Ag ) = m (A), where Ag is the set of elements equal to π(g,x) for some x in A.