Is it possible to define conditional expectations for probability charges?

被引：0
作者：
de Amo, Enrique [1 ]
Sempi, Carlo [2 ]
机构：
[1] Univ Almeria, Dept Matemat, Almeria 04120, Spain
[2] Univ Salento, Dipartimento Matemat & Fis Ennio De Giorgi, I-73100 Lecce, Italy
来源：
FUZZY SETS AND SYSTEMS | 2020年 / 379卷
关键词：
Charge; Integral; Conditional expectation; RADON-NIKODYM THEOREM;
D O I：
10.1016/j.fss.2019.01.016
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We propose a definition of conditional expectation in a finitely additive setting by relying on the theory of charges and circumventing the lack of an exact Radon-Nikodym theorem in this setting. We also show that the definition we propose satisfies most of the usual properties of Conditional Expectations in the traditional countably additive setting. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：37 / 47
页数：11
相关论文
共 19 条
[1]  
[Anonymous], 1966, Introduction to Measure and Probability
[2]  
Ash R.B., 2000, REAL ANAL PROBABILIT, V2
[3]  
Barbieri G., 2002, HDB MEASURE THEORY, P911
[4]  
Bhaskara Rao, 1983, THEORY CHARGES STUDY
[5]   Additive set functions on groups [J].
Bochner, S .
ANNALS OF MATHEMATICS, 1939, 40 :769-799
[6]   ON A RADON-NIKODYM THEOREM FOR FINITELY ADDITIVE SET FUNCTIONS [J].
DARST, RB ;
GREEN, E .
PACIFIC JOURNAL OF MATHEMATICS, 1968, 27 (02) :255-&
[7]   A Radon-Nikodym derivative for positive linear functionals [J].
de Amo, E. ;
Diaz Carrillo, M. .
STUDIA MATHEMATICA, 2009, 192 (01) :1-14
[8]  
De Amo E., 1999, APPROXIMATE RADON NI, V48, P443
[9]  
Dvurecenskij A., 2002, HDB MEASURE THEORY, VII, P827
[10]   A RADON-NIKODYM THEOREM FOR FINITELY ADDITIVE SET FUNCTIONS [J].
FEFFERMAN, C .
PACIFIC JOURNAL OF MATHEMATICS, 1967, 23 (01) :35-+
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