6533b82ffe1ef96bd129467e

RESEARCH PRODUCT

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

B. BongiornoLuisa Di PiazzaKazimierz Musiał

subject

Pettis integralDiscrete mathematicsPure mathematicsHenstock–Kurzweil integralApplied MathematicsGeneral MathematicsBanach spaceMeasure (mathematics)Schauder basisRadon–Nikodym theoremSettore MAT/05 - Analisi MatematicaHenstock-Kurzweil integral Henstock-Kurzweil-Pettis integral Henstock integral variational Henstock integral Pettis integralLocally integrable functionMathematicsUnit interval

description

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

yearjournalcountryeditionlanguage
2011-10-24Acta Mathematica Sinica, English Series
https://doi.org/10.1007/s10114-011-0614-6