Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis

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Abstract

Let X be a Banach space with a Schauder basis {en}, and let Φ(I)= ∑n en ∫I fn(t)dt bea finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the senseof Henstock–Kurzweil. Necessary and sufficient conditions are given for Φ to be the indefinite integral ofa Henstock–Kurzweil–Pettis (or Henstock, or variational Henstock) integrable function f:[0, 1] → X.
Lingua originaleEnglish
pagine (da-a)219-234
Numero di pagine16
RivistaDefault journal
Volume28 (2)
Stato di pubblicazionePublished - 2012

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Radon-Nikodym Derivative
Radon
Banach spaces
Henstock-Kurzweil Integral
Banach space
Derivatives
Schauder Basis
Interval
Necessary Conditions
Unit
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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abstract = "Let X be a Banach space with a Schauder basis {en}, and let Φ(I)= ∑n en ∫I fn(t)dt bea finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the senseof Henstock–Kurzweil. Necessary and sufficient conditions are given for Φ to be the indefinite integral ofa Henstock–Kurzweil–Pettis (or Henstock, or variational Henstock) integrable function f:[0, 1] → X.",
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T1 - Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis

AU - Bongiorno, Benedetto

AU - Di Piazza, Luisa

AU - Musiał, Kazimierz

PY - 2012

Y1 - 2012

N2 - Let X be a Banach space with a Schauder basis {en}, and let Φ(I)= ∑n en ∫I fn(t)dt bea finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the senseof Henstock–Kurzweil. Necessary and sufficient conditions are given for Φ to be the indefinite integral ofa Henstock–Kurzweil–Pettis (or Henstock, or variational Henstock) integrable function f:[0, 1] → X.

AB - Let X be a Banach space with a Schauder basis {en}, and let Φ(I)= ∑n en ∫I fn(t)dt bea finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the senseof Henstock–Kurzweil. Necessary and sufficient conditions are given for Φ to be the indefinite integral ofa Henstock–Kurzweil–Pettis (or Henstock, or variational Henstock) integrable function f:[0, 1] → X.

KW - Henstock integral

KW - Henstock-Kurzweil integral

KW - Henstock-Kurzweil-Pettis integral

KW - Pettis integral

KW - variational Henstock integral

UR - http://hdl.handle.net/10447/61863

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