Abstract
In this paper. We study composition operators on some Mobius invariant Banach function Spaces like Bloch and F(p, q, s) spaces. We give a Carleson measure characterization on F(p, q. s) spaces, then we use this Carleson measure characterization of the compact compositions oil F(p, q, s) spaces to show that every compact composition operator on F(p. q,s) spaces is compact on a Bloch space. Also, we give conditions to clarify when the converse holds.