Some results on monotone metric spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10285516" target="_blank" >RIV/00216208:11320/14:10285516 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21110/14:00242135
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2013.12.042" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2013.12.042</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2013.12.042" target="_blank" >10.1016/j.jmaa.2013.12.042</a>

Result language
angličtina
Original language name
Some results on monotone metric spaces
Original language description
We present some new results on monotone metric spaces. We prove that every bounded 1-monotone metric space in R-d has a finite 1-dimensional Hausdorff measure. As a consequence we obtain that each continuous bounded curve in R-d has a finite length if and only if it can be written as a finite sum of 1-monotone continuous bounded curves. Next we construct a continuous function f such that M has a zero Lebesgue measure provided the graph(f vertical bar M) is a monotone set in the plane. We finally construct a differentiable function with a monotone graph and unbounded variation. (C) 2013 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA201%2F08%2F0383" target="_blank" >GA201/08/0383: Function Spaces, Weighted Inequalities and Interpolation</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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