Non approximate derivability of the Takagi function

TL;DR

This paper proves that the Takagi function, a well-known continuous nowhere differentiable function, is also nowhere approximately derivable, highlighting its complex local behavior.

Contribution

It establishes the non-approximate derivability of the Takagi function, a novel property not previously proven.

Findings

Takagi function is nowhere approximately derivable

Reveals complex local structure of the Takagi function

Extends understanding of non-differentiability properties

Abstract

The Takagi function is a classical example of a continuous nowhere differentiable function. In this paper we prove that it is nowhere approximately derivable.