A property of Cesàro-Perron integrals
L. S. Bosanquet · Proceedings of the Edinburgh Mathematical Society · 1940
It is well known that if f(t) is (a) integrable in the Lebesgue sense, or more generally (b) integrable in the Perron sense, over every interval (α, β) interior to (a, b), and if exists, then f(t) is integrable in the Perron sense over (a, b) to the value (1·1).