It is shown that for the inclusion of factors corresponding to an inclusion of ergodic discrete measured equivalence relations , is normal in in the sense of Feldman-Sutherland-Zimmer () if and only if is generated by the normalizing groupoid of . Though this fact has been already obtained in , we reprove it here by a quite different method.
Takehiko YAMANOUCHI. "Normality for an inclusion of ergodic discrete measured equivalence relations in the von Neumann algebraic framework." J. Math. Soc. Japan 59 (4) 993 - 1009, October, 2007. https://doi.org/10.2969/jmsj/05940993