Manuharawati
In this paper, we defined a locally small Riemann sum (LSRS) property relative to volume function Θ of vector-valued function on a cell E in a nondiscrete locally compact metric space X. By the definition, if a function f has LSRS property relative to Θ on cell E is denoted by f ε LSRS (E,Θ), then it can be proved that: (i) if f,g LSRS (E,Θ), then f + g LSRS (E,Θ) and αf LSRS (E,Θ) for any real number α (ii) if f ε LSRS (E,Θ), then f is bounded on E; (iii) if f ε LSRS (E,v), then f is Henstock integrable relative to Θ on E; (iv) if (Y,||.||) is a complete normed space and f:E → Y is Henstock integrable relative to Θ, then f ε LSRS (E,Θ). © 2014 Manuharawati.
Department of Mathematics, Faculty of Mathematics and Natural Science, State University of Surabaya, Surabaya, East Java, Indonesia
