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arXiv · 1805.06919

Luzin-type properties and the difference quotient of a real function

Yuri Andreev·Trevor J Richards
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Abstract

We introduce the notion of the difference quotient set of a real valued function $f$ on a set $E\subset[0,1]$, and compare this set to the range of $f$ on $E$. We discuss the measure theoretic properties of both the range and the difference quotient set of $f$ over $E$ under different assumptions on $f$ and $E$.

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Yuri Andreev, Trevor J Richards. 2018-05-17. Luzin-type properties and the difference quotient of a real function. https://arxiv.org/abs/1805.06919

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