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

N strongly quasi invariant measure on double coset