Bakhvalov, A. N. The behavior of \(\Lambda\)-variation of a function of two variables in a neighborhood of a regular point. (English. Russian original) Zbl 1028.26010 Mosc. Univ. Math. Bull. 57, No. 1, 1-8 (2002); translation from Vestn. Mosk. Univ., Ser. I 2002, No. 1, 3-10 (2002). In the paper it is proved that if the function \(f(s,t)\) has a bounded \(\Lambda\)-variation [D. Waterman, Stud. Math. 44, No. 1, 107-117 (1972; Zbl 0237.42001)] on \( (x;x+\theta)\times (y;y+\theta)\) for some \(\theta>0\), then its \(\Lambda\)-variation with respect to \( (x;x+\varepsilon)\times (y;y+\varepsilon)\) tends to zero as \(\varepsilon\to+0\). Reviewer: L.N.Chernetskaja (Kyïv) MSC: 26B30 Absolutely continuous real functions of several variables, functions of bounded variation Keywords:bounded \(\Lambda\)-variation; neighborhood of a regular point Citations:Zbl 0237.42001 PDFBibTeX XMLCite \textit{A. N. Bakhvalov}, Mosc. Univ. Math. Bull. 57, No. 1, 3--10 (2002; Zbl 1028.26010); translation from Vestn. Mosk. Univ., Ser. I 2002, No. 1, 3--10 (2002)