Geodesic
Approximate symmetric variation and the Lusin $N$-property
Izvestiya. Mathematics , Tome 61 (1997) no. 4, pp. 831-841

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An example is constructed of a continuous function having an approximate symmetric derivative everywhere, yet not having the Lusin $N$-property. The same example proves the existence of a continuous function whose approximate variation on some set of measure zero is non-zero, but whose approximate symmetric variation on the same set is zero. 
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     author = {V. A. Skvortsov},
     title = {Approximate symmetric variation and the {Lusin} $N$-property},
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     number = {4},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_4_a7/}
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V. A. Skvortsov. Approximate symmetric variation and the Lusin $N$-property. Izvestiya. Mathematics , Tome 61 (1997) no. 4, pp. 831-841. http://geodesic.mathdoc.fr/item/IM2_1997_61_4_a7/