TY - JOUR
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
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
M3 - Article
SN - 1439-8516
VL - 28 (2)
SP - 219
EP - 234
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
ER -