Calculational error invalidating claimed sufficient conditions to obtain the traditional weak value in Dressel and Jordan’s “Contextual-value approach to the generalized measurement of observables”

The article [1] presents a theorem which gives sufficient conditions for a “general conditioned average” introduced in [3] to yield the traditional weak value in the limit of arbitrarily weak measurements. The “general conditioned average” corresponds to what would more usually be called a (preselected and) postselected weak measurement. Since there is only one theorem in that article, we will simply call it “Theorem”. Essentially the same result with the same attempted proof appears in different notation in [2]. This Comment notes a calculational error in a key lemma which invalidates the proof of the Theorem. The statement of the Theorem is too complicated to repeat here in full, so we state only enough of it to explain the error. It concerns a positive operator valued measure (POVM) denoted {Ey( )}, with the parameter y in a finite set of integers 1, . . . , N . The parameter > 0 describes the “weakness” of the measurement; smaller correspond to weaker measurements. To use the POVM to obtain the average value of an observable FX (readers can ignore the subscript X, which is an artifact of the paper’s unusual notation) one seeks so-called “contextual values” which the paper calls fY ( ; y) (again, the