Search results for " variational Henstock integral"
showing 3 items of 3 documents
On strongly measurable Kurzweil-Henstock type integrable functions
2009
We consider the integrability, with respect to the scalar Kurzweil-Henstock integral, the Kurzweil-Henstock-Pettis integral and the variational Henstock integral, of strongly measurable functions de ned as f = P1 n=1 xn [n;n+1),where (xn) belongs to a Banach space. Examples which indicate the difference between the scalar Henstock-Kurzweil integral and the Henstock- Kurzweil-Pettis integral and between the variational Henstock integral and the Henstock-Kurzweil-Pettis integral are given.
Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis
2011
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.
Strongly measurable Kurzweil-Henstock type integrable functions and series
2008
We give necessary and sufficient conditions for the scalar Kurzweil-Henstock integrability and the Kurzweil-Henstock-Pettis integrability of functions $f:[1, infty) ightarrow X$ defined as $f=sum_{n=1}^infty x_n chi_{[n,n+1)}$. Also the variational Henstock integrability is considered