Comparison of some trigonometric integrals II

Relations between trigonometric integrals such as Burkill’s SCP-integral, Marcinkiewicz and Zygmund’s MZ-integral, Preiss and Thomson’s AS-integral, are considered. We show that the inclusions P⊂CP⊂SCP⊂MZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{P}\subset \mathrm{CP}\subset \mathrm{SCP}\subset \mathrm{MZ}$$\end{document} remain proper, while the inclusions SCP⊂AS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SCP}\subset \mathrm{AS}$$\end{document}, AS⊃MZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{AS}\supset \mathrm{MZ}$$\end{document}, SCP⊃AS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SCP}\supset \mathrm{AS}$$\end{document} remain invalid over the class of functions with continuous primitives.