On linearity of pan-integral and pan-integrable functions space

0477549 - ÚTIA 2018 RIV US eng J - Článek v odborném periodiku
Ouyang, Y. - Li, J. - Mesiar, Radko
On linearity of pan-integral and pan-integrable functions space.
International Journal of Approximate Reasoning. Roč. 90, č. 1 (2017), s. 307-318. ISSN 0888-613X. E-ISSN 1873-4731
Institucionální podpora: RVO:67985556
Klíčová slova: linearity * monotone measure * Pan-integrable space
Obor OECD: Pure mathematics
Impakt faktor: 1.766, rok: 2017
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
Trvalý link: http://hdl.handle.net/11104/0274042