In two-dimensional spinor electrodynamics with nonvanishing fermion mass it is proved—using tesults of Brandt—that [j 0 un (x, t),j 1 un (y, t)]=+(i/π)e 0 2 ∂1 δ(x−y), where μ un (k) is the exact unrenormalized electromagnetic current. Implications for the exact solution of the vacuum polarization are discussed.