In his famous paper [7] Gersho stressed that the codecells of optimal
quantizers asymptotically make an equal contribution to the distortion of the
quantizer. Motivated by this fact, we investigate in this paper quantizers in
the scalar case, where each codecell contributes with exactly the same portion
to the quantization error. We will show that such quantizers of Gersho type -
or Gersho quantizers for short - exist for non-atomic scalar distributions. As
a main result we will prove that Gersho quantizers are asymptotically optimal
