Geodesic
Closedness of sum spaces and the generalized Schrödinger problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 576-590 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Some general closedness properties of sum spaces of measurable functions are established. As application one obtains existence and uniqueness results for solutions of the generalized Schrödinger problem under an integrability condition but without any topological or boundedness assumptions. They also allow to prove an interesting structural result for distributions with multivariate marginals, to prove existence results for optimal approximations in additive statistical models, and to give an extension of Kolmogorov's representation theorem for continuous functions of severalvariables. This extension implies that any locally bounded measurable function has an exact representation by a neural network with one hidden layer.
Keywords: dinger equation, sum spaces, additivemodels, multivariate marginals, Kolmogorov representation theorem.
Mots-clés : Schrö 
@article{TVP_1997_42_3_a8,
     author = {L. R\"uschendorf and W. Thomsen},
     title = {Closedness of sum spaces and the generalized {Schr\"odinger} problem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {576--590},
     year = {1997},
     volume = {42},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a8/}
}
TY  - JOUR
AU  - L. Rüschendorf
AU  - W. Thomsen
TI  - Closedness of sum spaces and the generalized Schrödinger problem
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1997
SP  - 576
EP  - 590
VL  - 42
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a8/
LA  - en
ID  - TVP_1997_42_3_a8
ER  - 
%0 Journal Article
%A L. Rüschendorf
%A W. Thomsen
%T Closedness of sum spaces and the generalized Schrödinger problem
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1997
%P 576-590
%V 42
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a8/
%G en
%F TVP_1997_42_3_a8
L. Rüschendorf; W. Thomsen. Closedness of sum spaces and the generalized Schrödinger problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 576-590. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a8/