Strange Functions in Real Analysis - Alexander Kharazishvili - Bog

Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods. Finally, he considers examples of functions whose existence cannot be established without the help of addition set-theoretical axioms. This edition includes five new chapters that provide more information on the structure of strange functions, nearly 70 new exercises that extend the discussions within the text, and a significantly expanded list of reference that incorporates recent works.