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Description
  • A metric space (X,d) is monotone if there is a linear order < on X and a constant c > 0 such that d(x,y)a parts per thousand broken vertical bar cd(x,z) for all x < y < zaX. Properties of continuous functions with monotone graph (considered as a planar set) are investigated. It is shown, for example, that such a function can be almost nowhere differentiable, but must be differentiable at a dense set, and that the Hausdorff dimension of the graph of such a function is 1.
  • A metric space (X,d) is monotone if there is a linear order < on X and a constant c > 0 such that d(x,y)a parts per thousand broken vertical bar cd(x,z) for all x < y < zaX. Properties of continuous functions with monotone graph (considered as a planar set) are investigated. It is shown, for example, that such a function can be almost nowhere differentiable, but must be differentiable at a dense set, and that the Hausdorff dimension of the graph of such a function is 1. (en)
Title
  • PROPERTIES OF FUNCTIONS WITH MONOTONE GRAPHS
  • PROPERTIES OF FUNCTIONS WITH MONOTONE GRAPHS (en)
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  • PROPERTIES OF FUNCTIONS WITH MONOTONE GRAPHS
  • PROPERTIES OF FUNCTIONS WITH MONOTONE GRAPHS (en)
skos:notation
  • RIV/00216208:11320/14:10283067!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • I, P(GA201/09/0067), S
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 40322
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/14:10283067
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • sigma-porous set; absolutely continuous function; approximate derivative; derivative; graph; continuous function; monotone metric space (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • HU - Maďarsko
http://linked.open...ontrolniKodProRIV
  • [3B683BE39136]
http://linked.open...i/riv/nazevZdroje
  • Acta Mathematica Hungarica
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 142
http://linked.open...iv/tvurceVysledku
  • Nekvinda, Aleš
  • Zindulka, Ondřej
  • Vlasák, Václav
  • Hrusak, Michael
  • Matrai, Tamás
http://linked.open...ain/vavai/riv/wos
  • 000330806700001
issn
  • 0236-5294
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/s10474-013-0367-z
http://localhost/t...ganizacniJednotka
  • 11320
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