On linearity of pan-integral and pan-integrable functions space
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On linearity of pan-integral and pan-integrable functions space
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Approximate Reasoning
ISSN
0888-613X
e-ISSN
—
Volume of the periodical
90
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
307-318
UT code for WoS article
000413380900017
EID of the result in the Scopus database
2-s2.0-85027842943