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 ¯.

@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},
     address = {Grenoble},
     volume = {20},
     number = {2},
     year = {1970},
     doi = {10.5802/aif.353},
     zbl = {0195.06102},
     mrnumber = {46 #4184},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.353/}
}
TY  - JOUR
AU  - Blumenthal, Robert M.
AU  - Corson, Harry H.
TI  - On continuous collections of measures
JO  - Annales de l'Institut Fourier
PY  - 1970
SP  - 193
EP  - 199
VL  - 20
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.353/
DO  - 10.5802/aif.353
LA  - en
ID  - AIF_1970__20_2_193_0
ER  - 
%0 Journal Article
%A Blumenthal, Robert M.
%A Corson, Harry H.
%T On continuous collections of measures
%J Annales de l'Institut Fourier
%D 1970
%P 193-199
%V 20
%N 2
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.353/
%R 10.5802/aif.353
%G en
%F 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. https://aif.centre-mersenne.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

Cité par Sources :