Rectification of sets in Euclidean spaces (Q685217)

The author discusses and criticizes traditional definitions of the arc length which require semi-continuity from below and is based on approximations of curves by inscribed broken lines. The author suggests symmetric definitions of lower and upper \(n\)-length (\(n\)-dimensional volumes) for a wide class of sets in Euclidean spaces. The main result establishes the additivity of the introduced lower and upper rectifying sums.