Invariant random subgroups of strictly diagonal limits of finite symmetric groups

We classify the ergodic invariant random subgroups of strictly diagonal limits of finite symmetric groups

Old and new results on normality

We present a partial survey on normal numbers, including Keane's contributions, and with recent developments in different directions.Comment: Published at http://dx.doi.org/10.1214/074921706000000248 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org