Some generalizations of the concept of length
The paper is devoted to two numerical characteristics of a nonrectifiable are \(\gamma\subset\mathbb{C}\) generalizing the notion of length. Geometrically, this notion can naturally be generalized as the least upper bound of the sums \(\sum\varphi(a_j)\), where \(a_j\) are the lengths of segments of a polygonal line inscribed in the curve \(\gamma\) and \(\varphi\) is a given function. The author provides conditions under which the generalized geometric rectifiability of a curve \(\gamma\) implies its generalized analytic rectifiability.
scientific article; zbMATH DE number 1927823