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

We summarize the general results of El Karoui [1981] on optimal stopping problems for processes which are measurable with respect to Meyer-σ-fields. Meyer-σ-fields are due to Lenglart [1980] and include the optional and predictable σ-field as special cases. Novel contributions of our work are path regularity results for Meyer measurable processes and limit results for Meyer-projections. We will also clarify a minor issue in the proof of the optimality result in El Karoui [1981]. These extensions were inspired and needed for the proof of a stochastic representation theorem in Bank and Besslich [2018a]. As an application of this theorem, we provide an alternative approach to optimal stopping in the spirit of Bank and F"ollmer [2003].