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On inductive limits of measure spaces and projective limits of Lp-spaces

Published online by Cambridge University Press:  26 February 2010

N. D. Macheras
N. D. Macheras
Affiliation:
Department of Statistics, Piraeus Graduate School of Industrial Studies, 40, Karaoli and Dimitriou Stret, 185 32 Piraeus, Greece.
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Extract

The existence of inductive limits in the category of (topological) measure spaces is proved. Next, permanence properties of inductive limits are investigated. If (X, , ) is the inductive limit of the measure spaces (X, , ), we prove, for 1 p 221E;, that LP(X, , ) is embeddible into the projectilimit of Lp(X, ,) in the category Ban, for p <, respectively in the category C* in the case p = +. As an application, we exten existence theorems of strong liftings to inductive limits.

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Type
Research Article
Information
Mathematika , Volume 36 , Issue 1 , June 1989 , pp. 116 - 130
Copyright
Copyright University College London 1989

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