101 Years of Vector Lattice Theory: A Vector Lattice-Valued Daniell Integral View Full Text


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Chapter Info

DATE

2021-04-07

AUTHORS

Jacobus J. Grobler

ABSTRACT

We show that the paper in which P.J. Daniell introduced his well-known integral, used modern Riesz space techniques to derive the properties of the integral and to prove a fundamental decomposition result for the integral. The latter result was proved a decade later by F. Riesz and was considered to be the origin of Riesz space theory. After a survey of Daniell’s paper, we generalize P.E. Protter’s version of the Lp-valued (0 ≤ p ≤∞) Daniell integral to a vector lattice-valued Daniell integral, following closely Daniell’s original method. A.C.M van Rooij and W.B. van Zuijlen also introduced integrals for functions with values in a partially ordered vector space a more general setting than the one we use. More... »

PAGES

173-192

Book

TITLE

Positivity and its Applications

ISBN

978-3-030-70973-0
978-3-030-70974-7

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-030-70974-7_8

DOI

http://dx.doi.org/10.1007/978-3-030-70974-7_8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1139863877


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