Rearrangement and convergence in spaces of measurable functions.

Caponetti, D.; Trombetta, A.; Trombetta, G.

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On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm

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In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions $({\tilde{B}}^{ϕ} a . p .)$ endowed with the Luxemburg norm.