The above argument shows explicitly why the surface terms can cancel, but lacks generality. Alternatively, one can treat the case of lossless surrounding media with radiation boundary conditions imposed via the limiting absorption principle (LAP): Taking the limit as the losses (the imaginary part of ε) go to zero. For any nonzero loss, the fields decay exponentially with distance and the surface integral vanishes, regardless of whether the medium is homogeneous. Since the left-hand side of the Lorentz reciprocity theorem vanishes for integration over all space with any non-zero losses, it must also vanish in the limit as the losses go to zero. (Note that the LAP implicitly imposes the Sommerfeld radiation condition of zero incoming waves from infinity, because otherwise even an arbitrarily small loss would eliminate the incoming waves and the limit would not give the lossless solution.)