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On one analogue of Lebesgue theorem on the differentiation of indefinite integral for functions of several variables. (English) Zbl 1054.26501
Summary: It is proved that an indefinite $$n$$-tuple integral of a summable function on the unit $$n$$-dimensional cube is differentiable almost everywhere, moreover, it has a strong gradient almost everywhere.

##### MSC:
 26B05 Continuity and differentiation questions 26B30 Absolutely continuous real functions of several variables, functions of bounded variation