This article is cited in 1 paper

Comparison of Some Trigonometric Integrals

P. A. Sworovsky^a, V. A. Skvortsov<sup>b

a</sup> Kazimierz Wielki University
^b Lomonosov Moscow State University

Abstract: We show that Preiss–Thomson's AS-integral is inconsistent with Burkill's SCP-integral, James' $\mathrm P^2$-integral, and Denjoy's totalization $\mathrm{T}_{2s}$ over the class of functions with continuous primitives.

Keywords: symmetric Cesàro derivative, approximate symmetric derivative, Denjoy's totalization $\mathrm T_{2s}$, Burkill's SCP-integral, Preiss–Thomson's AS-integral, James' $\mathrm P^2$-integral.

UDC: 517

Received: 13.07.2017
Revised: 15.11.2017

DOI: 10.4213/mzm11745

 English version: Mathematical Notes, 2018, 104:2, 303–308

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