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Currently displaying 1 – 2 of 2

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On relations among metric derived numbers

Martin Koc — 2009

Acta Universitatis Carolinae. Mathematica et Physica

On Kantorovich's result on the symmetry of Dini derivatives

Martin Koc; Luděk Zajíček — 2010

Commentationes Mathematicae Universitatis Carolinae

For $f : (a, b) \to ℝ$ , 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 $A \subset (a, b)$ ...

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