ABSTRACT

A path P is rectifiab le if its length is finite. We may think of a rectifiable path P as being generated by a constantly mov­ ing particle which travels a finite distance in Rn starting at some initial point and ending at some terminal point. During this trip the position of the particle is tracked by observers a whose clocks (φα, Κ α) can run at arbitrarily varying rates with arbitrary initial settings. The properties of P are just those which are the same for all observers.