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

Let X be a Banach space with a Schauder basis {e n }, and let .(I) = . .n=1 e n . I f n (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 . to be the indefinite integral of a Henstock-Kurzweil-Pettis (or Henstock, or variational Henstock) integrable function f: [0, 1] . X.