Kadec–Klee properties of some quasi-Banach function spaces

We study Kadec–Klee properties with respect to global (local) convergence in measure in quasi-Banach function spaces. First, we prove some general results which can be of independent interest. Next, we investigate these properties in symmetrizations E( *) . Finally, we apply general results to study these properties in Marcinkiewicz and Lorentz spaces.