# Extremal solutions of a general marginal problem

Commentationes Mathematicae Universitatis Carolinae (1991)

- Volume: 32, Issue: 4, page 743-748
- ISSN: 0010-2628

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topLinhartová, Petra. "Extremal solutions of a general marginal problem." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 743-748. <http://eudml.org/doc/247315>.

@article{Linhartová1991,

abstract = {The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.},

author = {Linhartová, Petra},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {marginal problem; marginal system; simplicial measure; set of marginal uniqueness; extreme point; marginal problem; marginal uniqueness; Hilbert's thirteenth problem},

language = {eng},

number = {4},

pages = {743-748},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Extremal solutions of a general marginal problem},

url = {http://eudml.org/doc/247315},

volume = {32},

year = {1991},

}

TY - JOUR

AU - Linhartová, Petra

TI - Extremal solutions of a general marginal problem

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1991

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 32

IS - 4

SP - 743

EP - 748

AB - The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.

LA - eng

KW - marginal problem; marginal system; simplicial measure; set of marginal uniqueness; extreme point; marginal problem; marginal uniqueness; Hilbert's thirteenth problem

UR - http://eudml.org/doc/247315

ER -

## References

top- Arnol'd V.I., On functions of three variables (in Russian), Dokl. Akad. Nauk USSR 114 (1957), 679-681. (1957) MR0111808
- Beneš V., Štěpán J., The support of extremal probability measures with given marginals, In: Math. Stat. and Prob. Theory A (1987), 33-41. (1987) MR0922685
- Beneš V., Štěpán J., Extremal Solutions in the Marginal Problem, In: Advances in Probability Distributions with Given Marginals, Kluwer Academic Publishers, Dodrecht, 1991, 189-207. MR1215952
- Douglas R.G., On extremal measures and subspace density, Michigan Math. J. 11 (1964), 243-246. (1964) Zbl0121.33102MR0185427
- Dunford N., Schwartz J.T., Linear Operators, Interscience Publishers Inc., New York, 1958. Zbl0635.47003MR0117523
- Ersov M., The Choquet theorem and stochastic equations, Analysis Math. 1 (1975), 259-271. (1975) MR0401995
- Hoffmann-Jørgensen J., The general marginal problem, Lecture Notes in Math. 1242: Functional Analysis II, Springer-Verlag, 1987, 77-367. MR0906272
- Kolmogorov A.N., On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition (in Russian), Dokl. Akad. Nauk USSR 114 (1957), 953-956. (1957) MR0111809
- Letac G., Representation des mesures de probabilité sur le produit de deux espaces denombrables, de marges données., Ann. Inst. Fourier 16 (1966), 497-507. (1966) Zbl0141.14801MR0200957
- Štěpán J., Simplicial Measures, In: Contributions to Statistics (J. Hájek Memorial Volume), Praha, 1977, 239-251. MR0561272
- Štěpán J., Probability Measures with Given Expectations, Proc. of the 2nd Prague Symp. on Asympt. Statistics, North Holland, 1979, 315-320. MR0571198
- Štěpán J., Weak Convergence in Probability Theory (in Czech), Charles University, Prague, 1988, Dr. Sc. dissertation.
- Štěpán J., Simplicial Measures and Sets of Uniqueness in Marginal Problem, Statistics and Decisions, 1991, to appear. MR1257863
- Weizsäcker H. von, Winkler G., Integral representation in the set of solutions of a generalized moment problem, Math. Ann. 246 (1979), 23-32. (1979) MR0554129

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