  Lavrentiev curves form a special class of rectifiable curves which includes
cusp-free piecewise smooth curves. We call a Lavrentiev curve Legendrian if the
integral of the contact form equals zero on any its subarc. We define
Legendrian isotopies of such curves and prove that the equivalence classes of
Legendrian Lavrentiev links with respect to Legendrian isotopies coincide with
smooth classes.
