no. 2
On continuous collections of measures
Annales de l'Institut Fourier, Tome 20 (1970) no. 2, pp. 193-199.

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 ¯.

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     author = {Blumenthal, Robert M. and Corson, Harry H.},
     title = {On continuous collections of measures},
     journal = {Annales de l'Institut Fourier},
     pages = {193--199},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {20},
     number = {2},
     year = {1970},
     doi = {10.5802/aif.353},
     mrnumber = {46 #4184},
     zbl = {0195.06102},
     language = {en},
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}
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Blumenthal, Robert M.; Corson, Harry H. On continuous collections of measures. Annales de l'Institut Fourier, Tome 20 (1970) no. 2, pp. 193-199. doi : 10.5802/aif.353. http://archive.numdam.org/articles/10.5802/aif.353/

[1] S. Bochner, Harmonic Analysis and the Theory of Probability, University of Cal. Press, Berkeley (1955). | MR | Zbl

[2] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, Princeton, N.J. (1941). | JFM | MR | Zbl

[3] N. T. Peck, Representation of Functions in C(X) by Means of Extreme Points, PAMS 18 (1967), 133-135. | MR | Zbl

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