# Article

 Title: A Hake-type property for the $\nu_1$-integral and its relation to other integration processes (English) Author: Jurkat, W. B. Author: Nonnenmacher, D. J. F. Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 45 Issue: 3 Year: 1995 Pages: 465-472 . Category: math . MSC: 26A39 MSC: 26B20 idZBL: Zbl 0852.26008 idMR: MR1344512 . Date available: 2009-09-24T09:49:25Z Last updated: 2016-04-07 Stable URL: http://hdl.handle.net/10338.dmlcz/128533 . Reference: [Fed] H. Federer: Geometric Measure Theory.Springer, New York, 1969. Zbl 0176.00801, MR 0257325 Reference: [Jar-Ku] J. Jarnik and J. Kurzweil: A non-absolutely convergent integral which admits transformation and can be used for integration on manifolds.Czech. Math. J. 35 (110) (1985), 116–139. MR 0779340 Reference: [JKS] J. Jarnik, J. Kurzweil and S. Schwabik: On Mawhin’s approach to multiple nonabsolutely convergent integral.Casopis Pest. Mat. 108 (1983), 356–380. MR 0727536 Reference: [Ju-No 1] W.B. Jurkat and D.J.F. Nonnenmacher: An axiomatic theory of non-absolutely convergent integrals in $R^n$.Fund. Math. 145 (1994), 221–242. MR 1297406 Reference: [Ju-No 2] W.B. Jurkat and D.J.F. Nonnenmacher: A generalized $n$-dimensional Riemann integral and the Divergence Theorem with singularities.Acta Sci. Math. (Szeged) 59 (1994), 241–256. MR 1285443 Reference: [Ju-No 3] W.B. Jurkat and D.J.F. Nonnenmacher: The Fundamental Theorem for the $\nu _1$-integral on more general sets and a corresponding Divergence Theorem with singularities.(to appear). MR 1314531 Reference: [Ku-Jar] J. Kurzweil and J. Jarnik: Differentiability and integrability in $n$ dimensions with respect to $\alpha$-regular intervals.Results in Mathematics 21 (1992), 138–151. MR 1146639, 10.1007/BF03323075 Reference: [No] D.J.F. Nonnenmacher: Every $M_1$-integrable function is Pfeffer integrable.Czech. Math. J. 43 (118) (1993), 327–330. MR 1211754 Reference: [Pf] W.F. Pfeffer: The Gauss-Green theorem.Adv. in Math. 87 (1991), no. 1, 93–147. Zbl 0732.26013, MR 1102966, 10.1016/0001-8708(91)90063-D Reference: [Saks] S. Saks: Theory of the integral.Dover, New York, 1964. MR 0167578 .

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