  The deterministic analog of the Markov property of a time-homogeneous Markov
process is the semigroup property of solutions of an autonomous differential
equation. The semigroup property arises naturally when the solutions of a
differential equation are unique, and leads to a semiflow. We prove an abstract
result on measurable selection of a semiflow for the situations without
uniqueness. We outline applications to ODEs, PDEs, differential inclusions,
etc. Our proof of the semiflow selection theorem is motivated by N. V. Krylov's
Markov selection theorem. To accentuate this connection, we include a new
version of the Markov selection theorem related to more recent papers of
Flandoli & Romito and Goldys et al.
