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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F17%3A00477549" target="_blank" >RIV/67985556:_____/17:00477549 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.ijar.2017.08.001" target="_blank" >http://dx.doi.org/10.1016/j.ijar.2017.08.001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijar.2017.08.001" target="_blank" >10.1016/j.ijar.2017.08.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

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

Popis výsledku anglicky

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

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Approximate Reasoning

ISSN

0888-613X

e-ISSN

—

Svazek periodika

90

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

307-318

Kód UT WoS článku

000413380900017

EID výsledku v databázi Scopus

2-s2.0-85027842943