Strongly extreme points in Orlicz spaces equipped with the pp-Amemiya norm

This paper is a continuation of the paper [Y. Cui, L. Duan, H. Hudzik, M. Wisła, Basic theory of pp-Amemiya norm in Orlicz spaces (1≤p≤∞)(1≤p≤∞): Extreme points and rotundity in Orlicz spaces equipped with these norms, Nonlinear Anal. 69 (2008) 1796–1816] and an extension of the paper [Y. Cui, T. Wang, Strongly extreme points of Orlicz space, J. Math. 4 (1987) 335-340]. Criteria for the Kadec–Klee property with respect to the convergence in measure and for strongly extreme points in Orlicz spaces LΦ,pLΦ,p equipped with thepp-Amemiya norm (1≤p≤∞)(1≤p≤∞) are given. Orlicz spaces with nonempty (and empty) set of strongly extreme points of the unit ball B(LΦ,p)B(LΦ,p) are characterized. It is interesting to note that for some Orlicz functions ΦΦ there is a critical number p0p0 such that the problem of emptiness or nonemptiness of strongly extreme points of the unit ball B(LΦ,p)B(LΦ,p) looks different for 1≤p≤p01≤p≤p0 and for p0