From the reviews:
“The author took up several of the crucial topics of measure theory and developed them according to his ‘new foundations of measure theory’. The author is offering twenty of his papers in this tome … . This collection of papers along with MI are a must on the bookshelves of any measure theorist. … On the whole the present volume will serve as a useful resource … in MI.” (K. P. S. Bhaskara Rao, Mathematical Reviews, April, 2013)
“The main body of this impressive volume is a collection of twenty-five papers whose sole author is Heinz König, an esteemed analyst. … the volume can be recommended to all those interested in the foundations of measure theory and stochastic processes.” (Zbigniew Lipecki, zbMATH, Vol. 1267, 2013)
This collection of Heinz König’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 Carathéodory 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 König 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).
