Lebesgue’s theorem of differentiation in Fréchet lattices
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- by Karl-Goswin Grosse-Erdmann PDF
- Proc. Amer. Math. Soc. 112 (1991), 371-379 Request permission
Abstract:
Lebesgue’s differentiation theorem (LDT) states that every monotonic real function is differentiable a.e. We investigate the validity of this theorem for functions with values in topological vector lattices. It is shown that a Fréchet lattice satisfies (LDT) iff it is isomorphic to a generalized echelon space, a Banach lattice satisfies (LDT) iff it is isomorphic to some ${l^1}\left ( \Gamma \right )$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 371-379
- MSC: Primary 46G05; Secondary 46A40
- DOI: https://doi.org/10.1090/S0002-9939-1991-1062390-3
- MathSciNet review: 1062390