A Lusin type theorem for regular monotone uniformly autocontinuous set multifunctions

In this paper, we continue our study concerning monotone (uniformly) autocontinuous regular set multifunctions. As an application, a Lusin type theorem under a suitable type of measurability is obtained and several applications for finitely purely atomic multisubmeasures are proved.

[1]  Deli Zhang,et al.  Generalized fuzzy integrals of set-valued functions , 1995, Fuzzy Sets Syst..

[2]  Congxin Wu,et al.  Fuzzy regular measures on topological spaces , 2001, Fuzzy Sets Syst..

[3]  Jun Li,et al.  Regularity of null-additive fuzzy measure on metric spaces , 2003, Int. J. Gen. Syst..

[4]  W. Congxin,et al.  On the regularity of the fuzzy measure on metric fuzzy measure spaces , 1994 .

[5]  Deli Zhang,et al.  On set-valued fuzzy integrals , 1993 .

[6]  Alina Gavrilut,et al.  Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Baire multivalued set functions , 2009, Fuzzy Sets Syst..

[7]  Alina Gavrilut,et al.  A fuzzy Gould type integral , 2010, Fuzzy Sets Syst..

[8]  Michio Sugeno,et al.  Regular fuzzy measure and representation of comonotonically additive functional , 2000, Fuzzy Sets Syst..

[9]  菅野 道夫,et al.  Theory of fuzzy integrals and its applications , 1975 .

[10]  Jun Li,et al.  Regularity Properties of Null-Additive Fuzzy Measure on Metric Spaces , 2005, MDAI.

[11]  Qingshan Jiang,et al.  Lebesgue and Saks decompositions of σ-finite fuzzy measures , 1995, Fuzzy Sets Syst..

[12]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[13]  Lusin type theorems for multifunctions, Scorza Dragoni's property and Carath'eodory selections , 1992 .

[14]  Radko Mesiar,et al.  Pseudo-Additive Measures and Triangular-Norm-Based Conditioning , 2002, Annals of Mathematics and Artificial Intelligence.

[15]  E. Pap Null-Additive Set Functions , 1995 .

[16]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

[17]  Divakaran Liginlal,et al.  Modeling attitude to risk in human decision processes: An application of fuzzy measures , 2006, Fuzzy Sets Syst..

[18]  Shouchuan Hu,et al.  Handbook of multivalued analysis , 1997 .

[19]  Alina Gavrilut,et al.  Regularity and autocontinuity of set multifunctions , 2010, Fuzzy Sets Syst..

[20]  Deli Zhang,et al.  On set-valued fuzzy measures , 2004, Inf. Sci..

[21]  Finitely purely atomic measures: Coincidence and rigidity properties , 2001 .

[22]  Jun Li,et al.  Lusin's theorem on fuzzy measure spaces , 2004, Fuzzy Sets Syst..

[23]  Xizhao Wang,et al.  Some notes on the regularity of fuzzy measures on metric spaces , 1997, Fuzzy Sets Syst..

[24]  N. Mastorakis,et al.  On different types of non-additive set multifunctions , 2009 .

[25]  A. C. Thompson,et al.  Theory of correspondences : including applications to mathematical economics , 1984 .

[26]  Jun Kawabe Regularity and Lusin's theorem for Riesz space-valued fuzzy measures , 2007, Fuzzy Sets Syst..

[27]  Siegfried Weber,et al.  Generalized measures , 1991 .

[28]  Qingshan Jiang,et al.  Fuzzy measures on metric spaces , 1996, Fuzzy Sets Syst..

[29]  N. Dinculeanu,et al.  CHAPTER I – VECTOR MEASURES , 1967 .