Most Monotone Functions are Singular

DOI10.2307/2320713zbMath0462.26004OpenAlexW4250690856MaRDI QIDQ3912993

Tudor I. Zamfirescu

Publication date: 1981

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2320713

zbMATH Keywords

singular functionsDini derivativesuniformly bounded variationfirst and second Baire categorystrictly increasing continuous functions

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Singular functions, Cantor functions, functions with other special properties (26A30) Monotonic functions, generalizations (26A48) Classification of real functions; Baire classification of sets and functions (26A21) Functions of bounded variation, generalizations (26A45) Topology of special sets defined by functions (54C50)

Related Items (13)

Systems of functional equations and generalizations of certain functions ⋮ Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ On singularity and fine spectral structure of random continued fractions ⋮ Is the optimal income tax regressive? ⋮ A certain modification of classical singular function ⋮ One class of continuous functionswith complicated local properties related to Engel series ⋮ Self-affine singular and nowhere monotone functions related to the \(Q\)-representation of real numbers ⋮ On the qualitative properties of the optimal income tax ⋮ Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians ⋮ On the Baire generic validity of the \(t\)-multifractal formalism in Besov and Sobolev spaces ⋮ Limit distributions for conflict dynamical system with point spectra ⋮ On distributions with fixed marginals maximizing the joint or the prior default probability, estimation, and related results ⋮ Typical monotone continuous functions

This page was built for publication: Most Monotone Functions are Singular