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 The action of special linear group on the set of mutually distinct triple points of circle and invariant measure Commun. Korean Math. Soc.Published online February 26, 2021 Sanghoon Kwon Catholic Kwandong University Abstract : We investigate the Mobius transformation action of $PSL(2,\mathbb{R})$ on the set of mutually distinct ordered triple points of $\mathbb{R}\cup\{\infty\}$. Keywords : invariant measure, special linear group, unit tangent bundle MSC numbers : Primary 37E35, Secondary 28D05. Full-Text :