  We classify which local problems with inputs on oriented paths have so-called
Borel solution and show that this class of problems remains the same if we
instead require a measurable solution, a factor of iid solution, or a solution
with the property of Baire.
  Together with the work from the field of distributed computing [Balliu et al.
PODC 2019], the work from the field of descriptive combinatorics [Gao et al.
arXiv:1803.03872, Bernshteyn arXiv:2004.04905] and the work from the field of
random processes [Holroyd et al. Annals of Prob. 2017, Greb\'ik, Rozho\v{n}
arXiv:2103.08394], this finishes the classification of local problems with
inputs on oriented paths using complexity classes from these three fields.
  A simple picture emerges: there are four classes of local problems and most
classes have natural definitions in all three fields.
  Moreover, we now know that randomness does \emph{not} help with solving local
problems on oriented paths.
