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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.
  • 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. (en)
Title
  • Some results on monotone metric spaces
  • Some results on monotone metric spaces (en)
skos:prefLabel
  • Some results on monotone metric spaces
  • Some results on monotone metric spaces (en)
skos:notation
  • RIV/00216208:11320/14:10285516!RIV15-MSM-11320___
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  • 45995
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  • RIV/00216208:11320/14:10285516
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  • Graphs of continuous functions; Hausdorff measure; Monotone metric spaces (en)
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  • US - Spojené státy americké
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  • [2BAC66F0CD17]
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  • Journal of Mathematical Analysis and Applications
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  • 413
http://linked.open...iv/tvurceVysledku
  • Vlasák, Václav
  • Pokorný, Dušan
  • Nekvinda, Ales
http://linked.open...ain/vavai/riv/wos
  • 000331344600032
issn
  • 0022-247X
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.jmaa.2013.12.042
http://localhost/t...ganizacniJednotka
  • 11320
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