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 $\overline{X}$ is shown to be the resolvent of a probability measure on the space of continuous functions from $M$ to $\overline{X}$.

@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},
pages = {193--199},
publisher = {Institut Fourier},
volume = {20},
number = {2},
year = {1970},
doi = {10.5802/aif.353},
zbl = {0195.06102},
mrnumber = {46 \#4184},
language = {en},
url = {www.numdam.org/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) no. 2, pp. 193-199. doi : 10.5802/aif.353. http://www.numdam.org/item/AIF_1970__20_2_193_0/

[1] S. Bochner, Harmonic Analysis and the Theory of Probability, University of Cal. Press, Berkeley (1955). | MR 17,273d | Zbl 0068.11702

[2] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, Princeton, N.J. (1941). | JFM 67.1092.03 | MR 3,312b | Zbl 0060.39808

[3] N. T. Peck, Representation of Functions in C(X) by Means of Extreme Points, PAMS 18 (1967), 133-135. | MR 34 #8167 | Zbl 0145.38102