Derivatives take every value on the set of approximate continuity points

DOI10.1007/BF01956783zbMath0542.26005MaRDI QIDQ795189

N. E. Zubov

Publication date: 1983

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

zbMATH Keywords

derivativesapproximately continuous functionsBaire 1 functionsDarboux Baire 1 functionsBanach space of bounded functionsset of approximate continuity points

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Classification of real functions; Baire classification of sets and functions (26A21)

Related Items

Approximate continuity points of derivatives of functions of several variables

Cites Work

• Most Darboux Baire 1 functions map big sets onto small sets
• Some typical results on bounded Baire 1 functions
• The Oscillatory Behavior of Certain Derivatives