Overview

This text draws together a number of recent results concerning barrelled locally convex spaces, from general facts involving cardinality and dimensionality to barrelledness of some familiar vector-valued or scalar-valued normed spaces of functional analysis, and providing a study of some of these spaces. Throughout the exposition, the authors show the strong relationship between barrelledness properties and vector-valued measure theory. The book is self-contained and addressed to researchers and graduate students with interests in barrelled convex spaces or measure theory. Since barrelled spaces are a keystone in functional analysis for the role they play as the domain class of fundamental results such as the Banach-Steinhaus and the closed graph theorem, this book should also be useful to readers generally interested in functional analysis.

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