This will be mostly a survey talk of the subject. I will discuss some interesting measures that can be used to study the Grothendieck ring of varieties. Applications to rationality of the motivic zeta function will be explained.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/5312