Fatemeh Fahimian - Department of Mathematics, Center of Excellecy in Analysis on Algebric Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, Iran
Rajab Ali Kamyabi Gol - Department of Mathematics, Center of Excellecy in Analysis on Algebric Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, Iran
Fatemeh Esmaeelzadeh - Department of Mathematics, Bojnourd Branch, Islamic Azad university, Bojnourd, Iran

Let G be a locally compact group, H and K be two closed subgroups of G, and N be the normalizer group of K in G. In this paper, the existence and properties of a rho-function for the triple (K, G, H) and an N-strongly quasi-invariant measure of double coset space K \backslash G /H is investigated. In particular, it is shown that any such measure arises from a rho-function. Furthermore, the conditions under which an N-strongly quasi-invariant measure arises from a rho-function are studied.

Double coset space, N-Strongly quasi invariant measure, rho-function