Some open mapping theorems for marginals

Author:
Larry Q. Eifler

Journal:
Trans. Amer. Math. Soc. **211** (1975), 311-319

MSC:
Primary 28A35; Secondary 60B05

MathSciNet review:
0387533

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Abstract: Let *S* and *T* be compact Hausdorff spaces and let and denote the collection of probability measures on *S, T* and , respectively. Given a probability measure on , set where and are the marginals of on *S* and *T*. We prove that the mapping is norm open and open. An analogous result for where and are probability spaces is established.

**[1]**Seymour Ditor Z. and Larry Q. Eifler,*Some open mapping theorems for measures*, Trans. Amer. Math. Soc.**164**(1972), 287–293. MR**0477729**, 10.1090/S0002-9947-1972-0477729-X**[2]**Paul R. Halmos,*Lectures on Boolean algebras*, Van Nostrand Mathematical Studies, No. 1, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. MR**0167440****[3]**Hans G. Kellerer,*Masstheoretische Marginalprobleme*, Math. Ann.**153**(1964), 168–198 (German). MR**0161956****[4]**Shu-Teh Chen Moy,*Characterizations of conditional expectation as a transformation on function spaces*, Pacific J. Math.**4**(1954), 47–63. MR**0060750****[5]**V. Strassen,*The existence of probability measures with given marginals*, Ann. Math. Statist.**36**(1965), 423–439. MR**0177430****[6]**L. Q. Eifler,*Open mapping theorems for probability measures on metric spaces*(to be submitted to Ann. Inst. Fourier, Grenoble).

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1975-0387533-1

Keywords:
Marginals,
open mapping theorems,
probability measures

Article copyright:
© Copyright 1975
American Mathematical Society