Bounded convergence theorem and integral operator for operator valued measures
The Denjoy extension of the Riemann and McShane integrals
In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval into a Banach space It is shown that a Denjoy-Bochner integrable function on is Denjoy-Riemann integrable on , that a Denjoy-Riemann integrable function on is Denjoy-McShane integrable on and that a Denjoy-McShane integrable function on is Denjoy-Pettis integrable on In addition, it is shown that for spaces that do not contain a copy of , a measurable Denjoy-McShane integrable...
The ap-Denjoy and ap-Henstock integrals
In this paper we define the ap-Denjoy integral and show that the ap-Denjoy integral is equivalent to the ap-Henstock integral and the integrals are equal.
The and -integrals
In this paper, we define the -integral of real-valued functions defined on an interval and investigate important properties of the -integral. In particular, we show that a function is -integrable on if and only if there exists an function such that almost everywhere on . It can be seen easily that every McShane integrable function on is -integrable and every -integrable function on is Henstock integrable. In addition, we show that the -integral is equivalent to the -integral....
The s-Perron, sap-Perron and ap-McShane integrals
In this paper, we study the s-Perron, sap-Perron and ap-McShane integrals. In particular, we show that the s-Perron integral is equivalent to the McShane integral and that the sap-Perron integral is equivalent to the ap-McShane integral.
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