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Mathematical Analysis Fundamentals by Agamirza Bashirov

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Chapter 8

Bounded Variation

Abstract

Chapter 8 concerns monotone functions and bounded variation. Basic properties of monotone functions are proved. Continuous and jump monotone functions are considered. Relationship of monotone and invertible functions is discussed. Example of a singular monotone function is presented. Monotone functions are generalized to functions of bounded variation. The space of functions of bounded variation is introduced. Continuous and jump functions of bounded variation are discussed. The chapter ends with the relation between bounded variation and rectifiable curves.

Keywords

Monotone function; bounded variation; space of functions of bounded variation; rectifiable curves

Functions of bounded variation, introduced by ...

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