Masse auf lokalbeschränkten Raümen

Dieter Sondermann

Annales de l'institut Fourier (1969)

  • Volume: 19, Issue: 2, page 33-113
  • ISSN: 0373-0956

Abstract

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The measure theory on a locally bounded space – i.e. a Hausdorff space with a “bounded” neighbourhood of each point – may be looked at from three different points of view. Firstly it is an extension of the measure theory of Bourbaki from locally compact spaces to more general topological spaces. Secondly from the point of view of the russian measure theorists Alexandroff, Prokhorov and Varadarajan it is an extension of their theory to measures which are not necessarily bounded. Finally the measure theory developed here may be regarded as the concrete version of the abstract theories of Stone and Loomis. This version is set up without leaving the original measure space by the introduction of ideal points – as is done by the well-known methods of compactification due to Kakutani and Bauer.The notion of integral developed in this article comprises – depending on the continuity properties of the measure considered – the Riemann integral as defined by Loomis, the first or the second Stone integral or – in case of a locally compact space – the Bourbaki integral. The different types of continuity of measures are characterized by making use of local compactification.The relations between the structure of a locally bounded space and the properties of his measures are studied in the last chapter. Different types of compactness are given a measure theoretic characterisation. Especially such a characterisation is given to the real compact spaces of Hewitt, since the results of some authors in this subject proved wrong. This result has some implications on the existence problem of measurable cardinals.

How to cite

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Sondermann, Dieter. "Masse auf lokalbeschränkten Raümen." Annales de l'institut Fourier 19.2 (1969): 33-113. <http://eudml.org/doc/73993>.

@article{Sondermann1969,
author = {Sondermann, Dieter},
journal = {Annales de l'institut Fourier},
keywords = {differentiation and integration, measure theory},
language = {ger},
number = {2},
pages = {33-113},
publisher = {Association des Annales de l'Institut Fourier},
title = {Masse auf lokalbeschränkten Raümen},
url = {http://eudml.org/doc/73993},
volume = {19},
year = {1969},
}

TY - JOUR
AU - Sondermann, Dieter
TI - Masse auf lokalbeschränkten Raümen
JO - Annales de l'institut Fourier
PY - 1969
PB - Association des Annales de l'Institut Fourier
VL - 19
IS - 2
SP - 33
EP - 113
LA - ger
KW - differentiation and integration, measure theory
UR - http://eudml.org/doc/73993
ER -

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