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Sep 14, 2021 at 6:37 vote accept AlbertRapp
Sep 9, 2021 at 19:12 answer added Yuval Peres timeline score: 1
Sep 9, 2021 at 13:26 answer added Iosif Pinelis timeline score: 3
Sep 9, 2021 at 12:46 comment added Dieter Kadelka Maybe I'm misssing something. The last question deals with the Cesaro limit of a squence (no probability needed). If the sequence converges then the Cesaro limit exists too and has the same value.
Sep 9, 2021 at 9:19 comment added AlbertRapp I tweaked the description a bit. Does this help? I am not sure that I understand what you refer to when you ask about the "what" of the sequences. Thes are in probability converging sequences of random variables. Unrelated to your remark, I added a modified question in the special case setting.
Sep 9, 2021 at 9:17 history edited AlbertRapp CC BY-SA 4.0
Tried make roles of $l$ and $n$ more apparend to show what qoes to infinity. Also added another part ot the special case question.
Sep 9, 2021 at 8:47 comment added Brendan McKay It isn't clear in your questions what your sequences are and what is going to infinity.
Sep 9, 2021 at 8:34 history edited YCor CC BY-SA 4.0
removed capitals, avoided abbreviation
Sep 9, 2021 at 7:18 history asked AlbertRapp CC BY-SA 4.0