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algebra arbitrary assume assumptions Banach space COMMENTATIONES MATHEMATICAE XXV compact continuous functions convergent Corollary Definition denote differential equations elements equivalent exists F-space finite formula Fourier series function f Hence holds hypergraph ideal implies indecomposable inequality integral isomorphism lattice Lebesgue measure Lemma Let F linear space linear topology locally bounded M-ideal MATEMATYCZNE XXV 1985 Math measurable function measure space modular spaces Moreover multifunctions N-function natural number neighbourhood non-negative norm obtain operator Orlicz function Orlicz spaces orthogonal series paper périodes principales Polon POLSKIEGO TOWARZYSTWA MATEMATYCZNEGO positive constant positive number PRACE MATEMATYCZNE XXV problem proof of Theorem properties Proposition prove pseudotopology real numbers respect ring ROCZNIKI POLSKIEGO TOWARZYSTWA satisfies condition satisfies the condition semicontinuous sequence solution strictly convex subset subspace summability Suppose symplectic Theorem topological spaces uniformly uniformly convergent vector space Warszawa XXVI zero