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《Journal of Baoji University of Arts and Sciences(Natural Science Edition)》 2009-01
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A research on equivalence between projection mapping and conditional expectation in L~2(Ω,F,P) space

YANG Ya-qiang1,YANG Yun-feng2(1.Department of Mathematics,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China;2.Department of Basic Courses,Xi'an University of Science and Technology,Xi'an 710054,Shaanxi,China)  
Aim The equivalence of the projection mapping and the conditional expectation in L2(Ω,F,P)space are investigated.Methods The equivalence is proved with logical inference method.Results It is proved that the projection mapping in L2(Ω,F,P)space is conditional expectation E(ξ|R).Conclusion The results show that the conditional expectation is the only projection mapping that meets the projection equation.
【Fund】: 宝鸡文理学院科研基金资助项目(zk0695)
【CateGory Index】: O177
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