no. 1
Limits of inverse systems of measures
Annales de l'Institut Fourier, Tome 21 (1971) no. 1, pp. 25-57.

Étant donné un système projectif d’espaces mesurés (X i ,μ i ) i∈I , on étudie le problème d’existence d’une limite projective en considérant d’abord une mesure μ ˜ définie sur le produit ∏ i∈I X i . Sous de simples conditions de régularité des μ i , on montre que μ ˜ a presque toutes les propriétés d’une limite. En outre, la limite projective μ ′ peut exister seulement si μ ˜ est elle-même une “limite” dans un sens plus général et μ ′ est alors la restriction de μ ˜ à l’ensemble limite des X i . On obtient des résultats plus forts que ceux connus jusqu’à présent en examinant cette restriction.

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.

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     title = {Limits of inverse systems of measures},
     journal = {Annales de l'Institut Fourier},
     pages = {25--57},
     publisher = {Institut Fourier},
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Mallory, J. D.; Sion, Maurice. Limits of inverse systems of measures. Annales de l'Institut Fourier, Tome 21 (1971) no. 1, pp. 25-57. doi : 10.5802/aif.361. https://aif.centre-mersenne.org/articles/10.5802/aif.361/

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