The Sharkovskiĭ Theorem for spaces of measurable functions

We formulate a generalization of the so-called Random Sharkovskiĭ Theorem from paper by Jan Andres, which is the randomized version of the classical Sharkovskiĭ Theorem. We use the method of transformation to deterministic case involving the Kuratowski–Ryll-Nardzewski selection theorem, which allows us to omit the assumption of completeness of the incorporated measurable space. Moreover, we formulate an analogue of the Sharkovskiĭ Theorem for spaces of measurable functions and for L p -spaces.