M. G. Plotnikov, “Generalized Riemann-Type Integrals on the Plane and an Example of Double Haar Series”, Mat. Zametki, 2009, Volume 86, Issue 4,Pages <nobr>601

Generalized Riemann-Type Integrals on the Plane and an Example of Double Haar Series

M. G. Plotnikov

Vologda State Academy of Milk Industry

Abstract: 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.

UDC: 517.518.3

Received: 21.01.2008
Revised: 26.09.2008

DOI: 10.4213/mzm4435