On Absolute Continuity of Non Negative Functions
Levi Otanga Olwamba *
Department of Mathematics, Actuarial and Physical Sciences University of Kabianga, P.O. BOX 2030-20200, Kericho, Kenya.
*Author to whom correspondence should be addressed.
Abstract
This paper is committed to the study of absolute continuity of non negative functions with respect to vector measures. Almost everywhere properties are applied to establish boundedness, measurability and convergence of sequences of measurable functions. The measurability of sets with respect to vector duality functions with values in a Hilbert space is considered.
Keywords: Measurable sets, absolute continuity, integrable functions, non-negative functions functions