On natural functions and Lipschitz functions.
Małolepszy, Marek
Real Anal. Exchange, Tome 28 (2002) no. 1, p. 249-258 / Harvested from Project Euclid
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We give certain characterizations of the so-called natural functions introduced by Chistyakov. We show that the set of natural functions from $[a, b]$ into a normed space $X$ is small in the porosity sense in the set of uniform Lipschitz 1 functions with the norm inherited from the space of $BV$ functions. The sizes of other classes of Lipschitz functions in $BV$ are also established.
Publié le : 2002-05-14
Classification:  bounded variation,  Lipschitz functions,  natural functions,  26A45,  26A16 
@article{1150118745,
     author = {Ma\l olepszy, Marek},
     title = {On natural functions and Lipschitz functions.},
     journal = {Real Anal. Exchange},
     volume = {28},
     number = {1},
     year = {2002},
     pages = { 249-258},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1150118745}
}

Małolepszy, Marek. On natural functions and Lipschitz functions.. Real Anal. Exchange, Tome 28 (2002) no. 1, pp.  249-258. http://gdmltest.u-ga.fr/item/1150118745/