Extremal and monogenic additive set functions

Plachky, Detlef

doi:10.1090/s0002-9939-1976-0419711-3

Cited by 44 publications

(17 citation statements)

References 9 publications

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“…The set of extreme points of E(P, A 1 , A 2 ) has been studied in great generality. We refer the reader to Lipecki (2007) and Plachky (1976) for further results and references.…”

Section: Appendix B: Merging Of Opinionsmentioning

confidence: 99%

Merging and testing opinions

Pomatto¹,

Al-Najjar

Sandroni

2014

Ann. Statist.

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We study the merging and the testing of opinions in the context of a prediction model. In the absence of incentive problems, opinions can be tested and rejected, regardless of whether or not data produces consensus among Bayesian agents. In contrast, in the presence of incentive problems, opinions can only be tested and rejected when data produces consensus among Bayesian agents. These results show a strong connection between the testing and the merging of opinions. They also relate the literature on Bayesian learning and the literature on testing strategic experts.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1212 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…The set of extreme points of E(P, A 1 , A 2 ) has been studied in great generality. We refer the reader to Lipecki (2007) and Plachky (1976) for further results and references.…”

Section: Appendix B: Merging Of Opinionsmentioning

confidence: 99%

Merging and testing opinions

Pomatto¹,

Al-Najjar

Sandroni

2014

Ann. Statist.

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“…Then is a strictly positive measure on A and an extreme extension of the measure (see Example 1 in [6] …”

Section: Existence Of Homomorphic Extensionsmentioning

confidence: 99%

“…3 and references therein). The properties of these extensions are studied in numerous works (see, e.g., [1][2][3][4][5][6][7][8]). …”

Section: Introductionmentioning

confidence: 99%

On one class of extreme extensions of a measure

Tarashchanskii

2011

Ukr Math J

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We consider a relationship between two sets of extensions of a finite finitely additive measure defined on an algebra B of sets to a broader algebra A: These sets are the set ex S of all extreme extensions of the measure and the set H of all extensions defined as .where O is a quotient measure on the algebra B= of the classes of -equivalence and hW A ! B= is a homomorphism extending the canonical homomorphism B to B= : We study the properties of extensions from H and present necessary and sufficient conditions for the existence of these extensions, as well as the conditions under which the sets ex S and H coincide.

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“…We shall need the following useful fact about extensions of measures. 11,15]). Let C ⊇ B be Boolean algebras and let µ be a measure on B.…”

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confidence: 99%