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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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