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Measure and Integration - Publications 1997-2011 (Paperback, 2012 ed.)
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Measure and Integration - Publications 1997-2011 (Paperback, 2012 ed.)
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This collection of Heinz Koenig's publications connects to his book
of 1997 "Measure and Integration" and presents significant
developments in the subject from then up to the present day. The
result is a consistent new version of measure theory, including
selected applications. The basic step is the introduction of the
inner * (bullet) and outer * (bullet) premeasures and their
extension to unique maximal measures. New "envelopes" for the
initial set function (to replace the traditional Caratheodory outer
measures) have been created, which lead to much simpler and more
explicit treatment. In view of these new concepts, the main results
are unmatched in scope and plainness, as well as in explicitness.
Important examples are the formation of products, a unified
Daniell-Stone-Riesz representation theorem, and projective limits.
Further to the contributions in this volume, after 2011 Heinz
Koenig published two more articles that round up his work: On the
marginals of probability contents on lattices (Mathematika 58, No.
2, 319-323, 2012), and Measure and integration: the basic extension
and representation theorems in terms of new inner and outer
envelopes (Indag. Math., New Ser. 25, No. 2, 305-314, 2014).
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