Abstract
Suppose given in the space ℝ = ℝ n an open set g. We denote by g1 its orthogonal projection on the hyperplane x1 = 0. Suppose given on g a real (complex) measurable function ƒ(x) = ƒ(x1, y). For fixed y it is a function of x1, defined on the corresponding open one-dimensional set. If ƒ is absolutely continuous on any closed finite segment belonging to this set, then we will say that it is for the indicated y locally absolutely continuous relative to x1.
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