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Article 11

Integrals of Lusin and Perron type

Real Analysis Exchange 14 (1989), 115-140.

Mathematical reviews subject classification: 26A39.

 

Abstract

In the first part of this paper, we study the relations between C. M. Lee's LDG and LPG-integrals (see An analogue of the theorem Hake-Alexandroff-Looman, Fund. Math. C (1978), 69-74) and the conditions  [M], [M] and [M].

We also give similar results for other integrals introduced here.

These results are then used to obtain change of variable formulae.

In the second part, we introduce an integral of Perron type, which is equivalent to the Foran integral.