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On Kantorovich's result on the symmetry of Dini derivatives

Martin KocLuděk Zajíček — 2010

Commentationes Mathematicae Universitatis Carolinae

For f : ( a , b ) , let A f be the set of points at which f is Lipschitz from the left but not from the right. L.V. Kantorovich (1932) proved that, if f is continuous, then A f is a “( k d )-reducible set”. The proofs of L. Zajíček (1981) and B.S. Thomson (1985) give that A f is a σ -strongly right porous set for an arbitrary f . We discuss connections between these two results. The main motivation for the present note was the observation that Kantorovich’s result implies the existence of a σ -strongly right porous set A ( a , b ) ...

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