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Mar 18, 2017 at 7:35 comment added Ori Gurel-Gurevich The thing here is not using the stationary measure (your proof becomes easier if we simply use counting measure), but using the case $r=1$. I've updated my answer accordingly.
Mar 18, 2017 at 7:33 history edited Ori Gurel-Gurevich CC BY-SA 3.0
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Mar 16, 2017 at 20:42 comment added Mikael de la Salle This graph is not volume doubling if, as in the question, one measures the volume of the ball as the number of edges (and not vertices) in the ball.
Mar 16, 2017 at 12:17 history answered Ori Gurel-Gurevich CC BY-SA 3.0