On the equivalence of McShane and Lebesgue integrals. (English) Zbl 0879.26029

It is known that a given function \(f:[a,b]\to \mathbb R\) is Lebesgue integrable on \([a,b]\) if and only if it is McShane integrable. (For the definition of the McShane integral, which is a sum type integral related to the Henstock-Kurzweil integral [see, e.g., Definition 16.7 in P.-Y. Lee, “Lanzhou lectures on Henstock integration” (1989; Zbl 0699.26004)] The author gives a new proof of this result which does not rely on measure theory. In particular, he does not make use of the Egoroff and Luzin theorems.
Reviewer: M.TvrdĂ˝ (Praha)


26A39 Denjoy and Perron integrals, other special integrals


Zbl 0699.26004