Limits of inverse systems of measures
Annales de l'Institut Fourier, Tome 21 (1971) no. 1, p. 25-57
Étant donné un système projectif d’espaces mesurés (X i ,μ i ) iI , on étudie le problème d’existence d’une limite projective en considérant d’abord une mesure μ ˜ définie sur le produit iI 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 iI 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.
@article{AIF_1971__21_1_25_0,
     author = {Mallory, J. D. and Sion, Maurice},
     title = {Limits of inverse systems of measures},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {21},
     number = {1},
     year = {1971},
     pages = {25-57},
     doi = {10.5802/aif.361},
     zbl = {0205.07101},
     mrnumber = {44 \#1782},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1971__21_1_25_0}
}
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. http://www.numdam.org/item/AIF_1971__21_1_25_0/

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