### 3.5 Influence of the measure

For the pure Einstein action, (12) with , some differences between the - and the
-measure were investigated on a 4^{4}-lattice by Beirl et al. [29, 30]. A constant-volume constraint
was used for simulations with the -measure, and a cutoff for . A study of the
-dependence of bulk geometric quantities agreed with previous simulations, wherever applicable. For
small , both measures lead essentially to identical results. For the -measure only, one
finds that and exhibit a jump at some , due to the formation of spikes
(isolated long link lengths, with the areas staying small). From this, and the study of edge
length distributions, one concludes that the DeWitt-type measure is generally better
behaved.