Limits of inverse systems of measures

J. D. Mallory; Maurice Sion

Annales de l'institut Fourier (1971)

  • Volume: 21, Issue: 1, page 25-57
  • ISSN: 0373-0956

Abstract

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In this paper the problem of the existence of an inverse (or projective) limit measure μ ' of an inverse system of measure spaces ( X i , μ i ) is approached by obtaining first a measure μ ˜ on the whole product space ∏ i ∈ I X i .The measure μ ˜ will have many of the properties of a limit measure provided only that the measures μ i possess mild regularity properties.It is shown that μ ' can only exist when μ ˜ is itself a “limit” measure in a more general sense, and that μ ' must then be the restriction of μ ˜ to the projective limit set L .Results stronger than those previously known are obtained by examining μ ˜ restricted to  L .

How to cite

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Mallory, J. D., and Sion, Maurice. "Limits of inverse systems of measures." Annales de l'institut Fourier 21.1 (1971): 25-57. <http://eudml.org/doc/74028>.

@article{Mallory1971,
abstract = {In this paper the problem of the existence of an inverse (or projective) limit measure $\mu ^\{\prime \}$ of an inverse system of measure spaces $(X_i,\mu _i)$ is approached by obtaining first a measure $\tilde\{\mu \}$ on the whole product space $\prod _\{i\in I\}X_i$.The measure $\tilde\{\mu \}$ will have many of the properties of a limit measure provided only that the measures $\mu _i$ possess mild regularity properties.It is shown that $\mu ^\{\prime \}$ can only exist when $\tilde\{\mu \}$ is itself a “limit” measure in a more general sense, and that $\mu ^\{\prime \}$ must then be the restriction of $\tilde\{\mu \}$ to the projective limit set $L$.Results stronger than those previously known are obtained by examining $\tilde\{\mu \}$ restricted to $L$.},
author = {Mallory, J. D., Sion, Maurice},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {25-57},
publisher = {Association des Annales de l'Institut Fourier},
title = {Limits of inverse systems of measures},
url = {http://eudml.org/doc/74028},
volume = {21},
year = {1971},
}

TY - JOUR
AU - Mallory, J. D.
AU - Sion, Maurice
TI - Limits of inverse systems of measures
JO - Annales de l'institut Fourier
PY - 1971
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 1
SP - 25
EP - 57
AB - In this paper the problem of the existence of an inverse (or projective) limit measure $\mu ^{\prime }$ of an inverse system of measure spaces $(X_i,\mu _i)$ is approached by obtaining first a measure $\tilde{\mu }$ on the whole product space $\prod _{i\in I}X_i$.The measure $\tilde{\mu }$ will have many of the properties of a limit measure provided only that the measures $\mu _i$ possess mild regularity properties.It is shown that $\mu ^{\prime }$ can only exist when $\tilde{\mu }$ is itself a “limit” measure in a more general sense, and that $\mu ^{\prime }$ must then be the restriction of $\tilde{\mu }$ to the projective limit set $L$.Results stronger than those previously known are obtained by examining $\tilde{\mu }$ restricted to $L$.
LA - eng
UR - http://eudml.org/doc/74028
ER -

References

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  16. [16] J.P. RAOULT, Sur une généralisation d'un théorème d'Ionescu Tulcea, C.R. Acad. Sc. Paris 259 (1964), 2769-2772. Zbl0133.39904MR32 #477
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