### Citations

265 | Tchebyche Systems: With Applications in Analysis and Statistics. - Karlin, Studden - 1966 |

207 | The markov moment problem and extremal problems. translations of mathematical monographs 50 - Krein, Nudelman - 1977 |

142 |
Lectures on Choquet Theorem
- Phelps
- 1966
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Citation Context ...is in exΛf ,C . At that, ∫ S gdµmax equals the left-hand side of (5). Thus, (5) follows. (ii, iii, iv): Suppose that condition (ii) of Proposition 6 holds. Then, by the Krein–Milman theorem (see e.g. =-=[8]-=-), condition (i) of the proposition holds as well. Thus, (5) follows. Note also that condition (iv) of Proposition 6 implies condition (iii), which in turn implies (ii). (v): Suppose that condition (v... |

21 |
Topology and Measure
- Topsøe
- 1970
(Show Context)
Citation Context ...] in most applications. The methods presented in this paper seem different from and more elementary than those of [15]. In particular, the present paper is self-contained, except for quoting [15] and =-=[13]-=- concerning part (v) of Proposition 6 and part (iv) of Proposition 9, respectively. As pointed out in [15], the results there generalize ones in Richter [11] (for S ⊆ R and piecewise-continuous fj’s),... |

15 |
The extrema of the expected value of a function of independent random variables
- Hoeffding
- 1955
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Citation Context ...ze ones in Richter [11] (for S ⊆ R and piecewise-continuous fj’s), Mulholland and Rogers [6] (for S = R), and Karr [4] (for compact metric spaces S). An equality similar to (7) was given by Hoeffding =-=[2]-=- for S = R; in fact, the result there holds for product measures on Rn. When S is an interval in R and the functions f1, . . . , fk, g form a Tchebycheff system, such results can be considerably impro... |

13 |
Extreme points of certain sets of probability measures, with applications
- Karr
- 1983
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Citation Context ...v) of Proposition 9, respectively. As pointed out in [15], the results there generalize ones in Richter [11] (for S ⊆ R and piecewise-continuous fj’s), Mulholland and Rogers [6] (for S = R), and Karr =-=[4]-=- (for compact metric spaces S). An equality similar to (7) was given by Hoeffding [2] for S = R; in fact, the result there holds for product measures on Rn. When S is an interval in R and the function... |

10 |
Extreme Points of Moment Sets
- Winkler
- 1988
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Citation Context ... equality (7) in Corollary 5, which holds without any topological assumptions. In conclusion, let us briefly discuss existing literature. The present paper was mainly motivated by the work of Winkler =-=[15]-=-, especially by the principal result there: Theorem 12. ([15, Theorem 2.1]). Suppose that the set Π of all probability measures in Λ is a Choquet-simplex and exΠ ⊆ ∆(1). Then the following conclusions... |

9 |
Representation theorems for distribution functions
- Mulholland, Rogers
- 1958
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Citation Context ... Proposition 6 and part (iv) of Proposition 9, respectively. As pointed out in [15], the results there generalize ones in Richter [11] (for S ⊆ R and piecewise-continuous fj’s), Mulholland and Rogers =-=[6]-=- (for S = R), and Karr [4] (for compact metric spaces S). An equality similar to (7) was given by Hoeffding [2] for S = R; in fact, the result there holds for product measures on Rn. When S is an inte... |

9 |
Sharp exponential estimates for sums of independent random variables. Theory Probab
- Pinelis, Utev
- 1989
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Citation Context ...-hand side of (7). So, (7) follows. The last sentence of Corollary 5 is proved quite similarly, using the last sentence of Corollary 4. Applications of equalities of the form (7) can be found e.g. in =-=[10]-=-. Let us now indicate a number of generic cases when condition (5) holds: Proposition 6. Condition (5) is satisfied in each of the following cases: (i) when there exists an extreme point of the set Λm... |

7 |
Integral representation in the set of solutions of a generalized moment problem
- Weizsäcker, Winkler
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Citation Context ...ition (iii), which in turn implies (ii). (v): Suppose that condition (v) of Proposition 6 holds. Then, by the arguments in [15, Theorems 3.1 and 3.2 and Proposition 3.1] (which in turn rely mainly on =-=[14]-=-), (5) follows. Iosif Pinelis/Extreme points of moments sets 6 Let us now supplement the results presented above by a few other ones, which are perhaps of lesser interest, in that they are not needed ... |

3 |
Parameterfreie abschätzung und realisierung von erwartungswerten
- Richter
- 1957
(Show Context)
Citation Context ...elf-contained, except for quoting [15] and [13] concerning part (v) of Proposition 6 and part (iv) of Proposition 9, respectively. As pointed out in [15], the results there generalize ones in Richter =-=[11]-=- (for S ⊆ R and piecewise-continuous fj’s), Mulholland and Rogers [6] (for S = R), and Karr [4] (for compact metric spaces S). An equality similar to (7) was given by Hoeffding [2] for S = R; in fact,... |

2 | Complete Spaces and Zero-One Measures - Adamski - 1976 |

2 | Supports of Borel measures - Okada - 1979 |

2 | Tchebycheff systems and extremal problems for generalized moments: a brief survey - Pinelis |

1 |
Supports of Borel measures
- Seidel
- 1989
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Citation Context ... if the condition that µ be a Radon measure were relaxed to it being regular; that is, if closed sets were used in place of compact sets K. For a further study of properties of support sets, see e.g. =-=[12]-=-. Proof of Proposition 9. For brevity, let SA := suppµA. (i): Suppose that A is a µ-atom, whereas SA contains two distinct points, say s1 and s2. Let G1 and G2 be open sets in S such that s1 ∈ G1, s2 ... |