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Pfeffer integrability does not imply \(M_ 1\)-integrability. (English) Zbl 0810.26009
After the introduction by the reviewer of an \(n\)-dimensional non-absolute integral which integrates the divergence of all differentiable vector fields on intervals, better ones have been introduced by Jarník, Kurzweil and Schwabik (\(M_ 1\)-integral), and by Pfeffer (Pf-integral). Nonnenmacher has recently shown that every \(M_ 1\)-integrable function is Pf-integrable. The present paper completes the comparison by constructing a function that if Pf-integrable but not \(M_ 1\)- integrable.

MSC:
26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
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References:
[1] D. J. F. Nonnenmacher: Every \(M_1\)-integrable function is Pfeffer integrable. Czechoslovak Math. J. 43(118) (1993) (to appear), 327-330. · Zbl 0789.26006
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