Article contents
A characterisation of multipliers for the Henstock–Kurzweil integral
Published online by Cambridge University Press: 26 April 2005
Abstract
It is proved that $fg$ is Henstock–Kurzweil integrable on a compact interval ${\mathop{\prod}_{i=1}^{m}}[a_i, b_i]$ in ${\mathbb R}^m$ for each Henstock–Kurzweil integrable function $f$ if and only if there exists a finite signed Borel measure $\nu$ on ${\mathop{\prod}_{i=1}^{m}}[a_i, b_i)$ such that $g$ is equivalent to $\nu({\mathop{\prod}_{i=1}^{m}}[a_i, \,{\cdot}\,))$ on ${\mathop{\prod}_{i=1}^{m}}[a_i, b_i]$.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 3 , May 2005 , pp. 487 - 492
- Copyright
- 2005 Cambridge Philosophical Society
- 4
- Cited by