Let X be a Banach space with a Schauder basis （en）, and let Ф（I） =∑^∞n=1 en ft fn（t）dt be a finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the sense of Hensto...Let X be a Banach space with a Schauder basis （en）, and let Ф（I） =∑^∞n=1 en ft 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 Ф to be the indefinite integral of a Henstock Kurzweil-Pettis （or Henstock, or variational Henstock） integrable function f ： [0, 1] → X.展开更多
基金Supported by the MURST of Italy(Prin2008)(Grant No.2008EEZ4N7)the Polish Ministry of Science and Higher Education of Poland(Grant No.N N201416139)
文摘Let X be a Banach space with a Schauder basis （en）, and let Ф（I） =∑^∞n=1 en ft 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 Ф to be the indefinite integral of a Henstock Kurzweil-Pettis （or Henstock, or variational Henstock） integrable function f ： [0, 1] → X.
