On sets where lip f is finite

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10405505" target="_blank" >RIV/00216208:11320/19:10405505 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=EP3ifwRSz~" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=EP3ifwRSz~</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm170820-26-5" target="_blank" >10.4064/sm170820-26-5</a>

Result language
angličtina
Original language name
On sets where lip f is finite
Original language description
Given a function f : R -> R, the so-called "little lip" function lip f is defined as follows: lip f(x) = lim inf(r -> 0) sup(|x - y| <= r) |f(y) - f(x)| / r. We show that if f is continuous on R, then the set where lip f is infinite is a countable union of countable intersections of closed sets (that is, an F-sigma delta set). On the other hand, given a countable union E of closed sets, we construct a continuous function f such that lip f is infinite exactly on E. A further result is that, for a typical continuous function f on the real line, lip f vanishes almost everywhere.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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