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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 \(\varepsilon\to+0\).

MSC:

26B30 Absolutely continuous real functions of several variables, functions of bounded variation

Citations:

Zbl 0237.42001
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