Research Article

Fubini’s theorem for a vector-valued Daniell integral

Published in: Quaestiones Mathematicae
Volume 47 , issue 7 , 2024 , pages: 1429–1435

DOI: 10.2989/16073606.2024.2322684

Author(s): Jacobus J. Grobler North-West University, South Africa

Keywords: 06F20 , 46A40 , 28A35 , 28B05 , Fubini’s theorem , product integral , Riesz space , Archimedean tensor product

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Abstract

We define the product integral for two Riesz space-valued Daniell integrals and prove Fubini’s theorem establishing the relation between product integrals and iterated integrals. The properties of the Fremlin tensor product of two Archimedean Riesz spaces enable one to do this in an elegant way.

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