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The Nevo–Zimmer theorem classifies the possible intermediate -factors  in , where  is a higher rank semisimple Lie group,  a minimal parabolic and  an irreducible -space with an invariant probability measure. An important corollary is the Stuck–Zimmer theorem, which states that a faithful irreducible action of a higher rank Kazhdan semisimple Lie group with an invariant probability measure is either transitive or free, up to a null set. We present a different proof of the first theorem, that allows us to extend these two well-known theorems to linear groups over arbitrary local fields.

The Nevo–Zimmer intermediate factor theorem over local fields