0477549 20240103214441.420170905235959.9 85027842943 000413380900017 10.1016/j.ijar.2017.08.001 12 s. P cav_un_epca*02567740888-613X901 (2017)307-318Elsevier linearity monotone measure Pan-integrable space cav_un_auth*0258953 30 Ouyang Y. CN K cav_un_auth*0348640 Li J. CN cav_un_auth*0101163 Ekonometrie Department of Econometrics E E Department of Econometrics 40 Mesiar Radko UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2017/E/mesiar-0477549.pdf This paper investigates the linearity and integrability of the (+, center dot)based pan-integrals on subadditive monotone measure spaces. It is shown that all nonnegative pan-integrable functions form a convex cone and the restriction of the pan-integral to the convex cone is a positive homogeneous linear functional. We extend the pan-integral to the general real-valued measurable functions. The generalized pan-integrals are shown to be symmetric and fully homogeneous, and to remain additive for all pan-integrable functions. Thus for a subadditive monotone measure the generalized pan-integral is linear functional defined on the linear space which consists of all pan-integrable functions. We define a p-norm on the linear space consisting of all p-th order pan-integrable functions, and when the monotone measure pi, is continuous we obtain a complete normed linear space L-pan(p) (X, t) equipped with the p-norm, i.e., an analogue of classical Lebesgue space L-P BA 10000 10100 10101 2018 3 RVO:67985556 http://hdl.handle.net/11104/0274042 S 3+4 Article Computer Science Artificial Intelligence 3+4 Article Computer Science Artificial Intelligence 3+4 Article Computer Science Artificial Intelligence COMPUTERSCIENCE.ARTIFICIALINTELLIGENCE 2.504 0.687 7.8 0.0042 0.658 3384 0.866 1.343 182 Q2 44.33 51.1 Q3 Q2 0.9 Q2 51.136 2017 85027842943 SCOPUS PUBMED 000413380900017 WOS cav_un_epca*0256774 International Journal of Approximate Reasoning 0888-613X 1873-4731 Roč. 90 č. 1 2017 307 318 Elsevier