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We summarize the general results of El Karoui [1981] on optimal stoppingproblems for processes which are measurable with respect toMeyer-$\sigma$-fields. Meyer-$\sigma$-fields are due to Lenglart [1980] andinclude the optional and predictable $\sigma$-field as special cases. Novelcontributions of our work are path regularity results for Meyer measurableprocesses and limit results for Meyer-projections. We will also clarify a minorissue in the proof of the optimality result in El Karoui [1981]. Theseextensions were inspired and needed for the proof of a stochasticrepresentation theorem in Bank and Besslich [2018a]. As an application of thistheorem, we provide an alternative approach to optimal stopping in the spiritof Bank and F{\"o}llmer [2003].

On Lenglart's Theory of Meyer-sigma-fields and El Karoui's Theory of Optimal Stopping