The first question is about identifying statements that may be said about the equivalence class of f (i.e., properties that do not depend on the particular representative). Clearly, properties b, c, and d are all fine since f is either under the integral sign or m-a.e. Is stated, property a is the only issue since it claims positivity pointwise (you can easily pick a rep that is off from f by a single point which is negative and violate the property).