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Totally ordered measure spaces and their Lp algebras

Part of: Set functions and measures on spaces with additional structure

Published online by Cambridge University Press:  26 February 2010

J. W. Baker ,
J. S. Pym  and
H. L. Vasudeva
J. W. Baker
Affiliation:
Department of Mathematics, University of Sheffield, Sheffield. S3 7RH
J. S. Pym
Affiliation:
Department of Mathematics, University of Sheffield, Sheffield. S3 7RH
H. L. Vasudeva
Affiliation:
Department of Mathematics, Punjab University, Chandigarh, India 160014.
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Extract

This paper is concerned with two aspects of the theory of measures on compact totally ordered spaces (the topology is to be the order topology). In Section 2, we clarify a recent construction of Sapounakis [11, 12] and, in so doing, we are able to say a little more about it. It should be added here that Sapounakis had other ends in view. To be precise, let I be the closed unit interval [0, 1] and let λ be Lebesgue measure on I. We shall construct another totally ordered set Ĩ which is compact in its order topology, a continuous increasing surjection τ : Ĩ → I with the property that card τ−1(t) = 2 for all t ∈ ]0,1[ (these brackets denote the open interval), and a measure on Ĩ such that τ() = λ. Then the following theorem holds.

MSC classification

Secondary: 28C99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 42 - 54
Copyright
Copyright © University College London 1982

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