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For a BV space function, this is the set where no finite approximate mean limit of a function exists. Its difference from the jump set of a bounded-variation function has zero $(n-1)$-dimensional Hausdorff measure.

An approximate mean limit of a function is a value satisfying the displayed condition. Functions in the BV space have such finite limits outside an approximate discontinuity set up to negligible sets in the appropriate measure. Their approximate jump points instead have two distinct half-ball limits.