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- W1587651452 abstract "Inspired by some results of Laυrič (1992), we investigate those Banach lattices E that have the following property (λ): Every increasing function f : [0, 1] → E has only countably many points of discontinuity. We show that the space of regular functions on [0, 1] contains no copy of ℓ∞ and yet it lacks property (λ), thus answering in the negative a question of Lavrič. On the positive part, our main results show that if a Banach lattice E has property (λ), then so do the Banach lattices C(K,E) and Lp(μ,E) (1 < p < ∞) for a wide class of compact spaces K and every measure μ." @default.
- W1587651452 created "2016-06-24" @default.
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- W1587651452 date "2001-01-01" @default.
- W1587651452 modified "2023-09-26" @default.
- W1587651452 title "Continuity of monotone functions with values in Banach lattices" @default.
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- W1587651452 doi "https://doi.org/10.1016/s0304-0208(01)80045-1" @default.
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