Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19369120221101N-strongly quasi-invariant measure on double coset spacesئ678469848210.22072/wala.2022.550186.1370ENFatemehFahimianDepartment of Mathematics, Center of Excellecy in Analysis on Algebric Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, IranRajab AliKamyabi GolDepartment of Mathematics, Center of Excellecy in Analysis on Algebric Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, IranFatemehEsmaeelzadehDepartment of Mathematics, Bojnourd Branch, Islamic Azad university, Bojnourd, IranJournal Article20220307Let $G$ 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. https://wala.vru.ac.ir/article_698482_eb0b55dc660364225d2ae4732c709657.pdf