On continuous collections of measures
Blumenthal, Robert M. ; Corson, Harry H.
Annales de l'Institut Fourier, Tome 20 (1970), p. 193-199 / Harvested from Numdam
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On démontre un théorème de représentation intégrale. Toute application continue d’un espace compact totalement discontinu M dans l’ensemble des mesures de probabilité sur un espace métrique complet X est la résolvante d’une mesure de probabilité sur l’espace des applications continues de M dans X.

An integral representation theorem is proved. Each continuous function from a totally disconnected compact space M to the probability measures on a complete metric space X ¯ is shown to be the resolvent of a probability measure on the space of continuous functions from M to X ¯.

@article{AIF_1970__20_2_193_0,
     author = {Blumenthal, Robert M. and Corson, Harry H.},
     title = {On continuous collections of measures},
     journal = {Annales de l'Institut Fourier},
     volume = {20},
     year = {1970},
     pages = {193-199},
     doi = {10.5802/aif.353},
     mrnumber = {46 \#4184},
     zbl = {0195.06102},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1970__20_2_193_0}
}

Blumenthal, Robert M.; Corson, Harry H. On continuous collections of measures. Annales de l'Institut Fourier, Tome 20 (1970) pp. 193-199. doi : 10.5802/aif.353. http://gdmltest.u-ga.fr/item/AIF_1970__20_2_193_0/

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