  The Ashtekar-Barbero formulation of general relativity admits a one-parameter
family of canonical transformations that preserves the expressions of the Gauss
and diffeomorphism constraints. The loop quantization of the connection
formalism based on each of these canonical sets leads to different predictions.
This phenomenon is called the Immirzi ambiguity. It has been recently argued
that this ambiguity could be generalized to the extent of a spatially dependent
function, instead of a parameter. This would ruin the predictability of loop
quantum gravity. We prove that such expectations are not realized, so that the
Immirzi ambiguity introduces exclusively a freedom in the choice of a real
number.
