Sets with Distinct Sums of Pairs, Long Arithmetic Progressions, and Continuous Mappings

We show that if φ : ℝ → ℝ is a continuous mapping and the set of nonlinearity of φ has nonzero Lebesgue measure, then φ maps bijectively a certain set that contains arbitrarily long arithmetic progressions onto a certain set with distinct sums of pairs.

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Bibliographic Details
Published inAnalysis mathematica (Budapest) Vol. 44; no. 3; pp. 369 - 380
Main Author Lebedev, V.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2018
Springer Nature B.V
Subjects
Analysis
Mathematics
Mathematics and Statistics
thin set
primary 43A46
long arithmetic progression
set with distinct sums of pairs
secondary 42A75
set of type Λ
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Summary:We show that if φ : ℝ → ℝ is a continuous mapping and the set of nonlinearity of φ has nonzero Lebesgue measure, then φ maps bijectively a certain set that contains arbitrarily long arithmetic progressions onto a certain set with distinct sums of pairs.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-018-0506-4