Let be a compact ordered space and let be two probabilities on such that for every increasing continuous function . Then we show that there exists a probability on such that
(i) , where is the graph of the order in ,
(ii) the projections of onto are and .
This theorem is generalized to the completely regular ordered spaces of Nachbin and also to certain infinite products. We show how these theorems are related to certain results of Nachbin, Strassen and Hommel.
Soit un espace compact ordonné et soient deux probabilités sur telles que pour toute fonction croissante continue . Alors nous démontrons qu’il existe une probabilité sur telle que :
(i) , où est le graphe de l’ordre sur ,
(ii) les projections de sur sont et .
On généralise ce théorème aux espaces complètement réguliers ordonnés de Nachbin et, en plus, à certains produits infinis. On met en évidence les relations entre ces résultats et les travaux de Nachbin, Strassen et Hommel.
@article{AIF_1978__28_4_53_0, author = {Edwards, David Albert}, title = {On the existence of probability measures with given marginals}, journal = {Annales de l'Institut Fourier}, pages = {53--78}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {28}, number = {4}, year = {1978}, doi = {10.5802/aif.717}, zbl = {0377.60004}, mrnumber = {81i:28009}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.717/} }
TY - JOUR AU - Edwards, David Albert TI - On the existence of probability measures with given marginals JO - Annales de l'Institut Fourier PY - 1978 SP - 53 EP - 78 VL - 28 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.717/ DO - 10.5802/aif.717 LA - en ID - AIF_1978__28_4_53_0 ER -
%0 Journal Article %A Edwards, David Albert %T On the existence of probability measures with given marginals %J Annales de l'Institut Fourier %D 1978 %P 53-78 %V 28 %N 4 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.717/ %R 10.5802/aif.717 %G en %F AIF_1978__28_4_53_0
Edwards, David Albert. On the existence of probability measures with given marginals. Annales de l'Institut Fourier, Volume 28 (1978) no. 4, pp. 53-78. doi : 10.5802/aif.717. https://aif.centre-mersenne.org/articles/10.5802/aif.717/
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