Convergence theorems for approximate mean continuous integral (Q1332581)

This is a continuation of an earlier paper by the same authors [Acta Math. Hung. 64, No. 3, 247-267 (1994; preceding review)] in which the \(D_ 1\)-integral was defined. In this paper, the authors proved the controlled convergence theorem and the generalized dominated convergence theorem for the \(D_ 1\)-integral. The \(D_ 1\)-integral is not compatible with the AP-integral of Burkill and the Kubota integral though it includes the Cesàro-Perron integral.