|Uniform hyperfiniteness is a strong version of hyperfiniteness, which can be defined for both infinite graphs and measured graphs. It turns out that in the case
of infinite graphs, uniform hyperfiniteness is equivalent to Property A. This fact leads to a positive answer of a conjecture of Brodzki et. al. about the equivalence of Property A and Uniform Local Amenability. For measured graphs, we have a uniform version of the
I will present some proofs and several, hopefully interesting, examples.