# Limits of inverse systems of measures

Annales de l'institut Fourier (1971)

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

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topMallory, 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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