Geodesic
Generalized Riemann-Type Integrals on the Plane and an Example of Double Haar Series
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 601-611

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We prove that du Bois-Reymond-type theorems do not hold for the double Haar series, for the dyadic cubic Henstock integral, and for regular convergence over rectangles.
Keywords: Riemann-type integral, double Haar series, dyadic cubic Henstock integral, regular convergence, du Bois-Reymond theorem, Fourier series. 
@article{MZM_2009_86_4_a11,
     author = {M. G. Plotnikov},
     title = {Generalized {Riemann-Type} {Integrals} on the {Plane} and an {Example} of {Double} {Haar} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {601--611},
     publisher = {mathdoc},
     volume = {86},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a11/}
}
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M. G. Plotnikov. Generalized Riemann-Type Integrals on the Plane and an Example of Double Haar Series. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 601-611. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a11/