Ordinalzahlen in der Analysis und Maßtheorie

Deiser, Oliver

doi:10.1007/s00591-007-0020-4

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2009

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Cited by 3 publications

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“…It is certainly worth a revival in a modern form. The first recent transfinite measure construction seems to be [7], which was unaware of the work done by Fox and others. While the primary aim of the construction in that paper was to Recently and importantly, lattices have been strongly advocated in measure theory by Heinz König (cf.…”

Section: Introductionmentioning

confidence: 99%

Measure theory based on lattices and transfinite recursion

Deiser

2009

Arch. Math.

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In this methodological study we develop the foundations of measure theory using lattices as prime structures instead of rings. Topological as well as abstract regularity is incorporated into this approach from the outset. The use of inner and outer measures is replaced by transfinite constructions. Basic extension steps are transfinitely iterated to yield generalizations of Carathéodory's theorem which are optimal with respect to inner and outer approximations. Mathematics Subject Classification (2000). 28A12, 28C20, 06B99.

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Section: Introductionmentioning

confidence: 99%