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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Lebesgue's theorem of differentiation in Fréchet lattices


Author: Karl-Goswin Grosse-Erdmann
Journal: Proc. Amer. Math. Soc. 112 (1991), 371-379
MSC: Primary 46G05; Secondary 46A40
MathSciNet review: 1062390
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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)$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062390-3
Keywords: Differentiation, monotonic functions, Gel'fand property, locally convex vector lattices, generalized AL-spaces, Köthe spaces, Köthe sequence spaces
Article copyright: © Copyright 1991 American Mathematical Society