INTEGRAL DUNFORD–HENSTOCK PADA SEL [a,b ]; DUNFORD–HENSTOCK INTEGRAL ON A CELL [a,b ]

SOLIKHIN, Soeparna Darmawijaya

2011 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

In this thesis, we construct Dunford-Henstock integral on a cell [a,b ] . Given X Banach space with * X is its dual space and [ , ] n a b ? ? cell. A function f :[a,b]?X is said to be Dunford-Henstock integrable on [a,b ] if for each * * x ?X the function * x f is Henstock integrable on [a,b ] and for each A?[a,b] measurable-? the function * x f is Henstock integrable on A , i.e., the function * A x f ? is Henstock integrable on [a,b ] . It will be shown that for each measurable-? A?[a,b] and * * x ?X there exists a unique * * Ax ? X such that * * * ( ) ( ) ( ) b A A a A x f ? H ? x f ? H ? x f Futhermore, we discuss some elementary properties and convergence theorems for the Dunford-Henstock integral on [a,b ] .

Kata Kunci : integral Dunford – Henstok