Timeline for Existence of a positive measurable set with disjoint preimage under iterated transformation

13 events

when toggle format	what		by	license	comment
Apr 21 at 0:07	comment	added	Saúl RM		@KhashF those sets are not measurable
Apr 20 at 22:58	comment	added	KhashF		If the map from your counter example is to be measure preserving, all subsets $\{i\}\times S^1 \,(i\in\Bbb{Z})$ must have the same measure . But their measures must add up to $\mu(\Bbb{Z}\times S^1)=1$.
Apr 20 at 21:49	comment	added	Saúl RM		Thanks for catching that, I added it explicitly
Apr 20 at 21:48	history	edited	Saúl RM	CC BY-SA 4.0	added 85 characters in body
Apr 20 at 21:19	comment	added	KhashF		@SaúlRM What is the probability measure in your counter example?
Apr 20 at 21:04	history	edited	Saúl RM	CC BY-SA 4.0	added 500 characters in body
Apr 20 at 19:37	vote	accept	abcdmath
Apr 20 at 19:41
Apr 20 at 12:30	history	edited	Saúl RM	CC BY-SA 4.0	added 951 characters in body
Apr 20 at 12:25	comment	added	Saúl RM		Yes, I added a more detailed explanation
Apr 20 at 12:25	history	edited	Saúl RM	CC BY-SA 4.0	added 951 characters in body
Apr 20 at 10:24	comment	added	abcdmath		thank you.But could you please explain the last line of the second-to-last paragraph? that is, how $\mu(\bigcup_{i,j} T^{-kj}A\Delta T^{-ki}A)=0$ and also with $B_n$ and from there how can we assume $T^{-k}A=A$ and $T^{-k}B_n=B_n$?
Apr 19 at 21:45	history	edited	Saúl RM	CC BY-SA 4.0	fixed typo
Apr 19 at 21:04	history	answered	Saúl RM	CC BY-SA 4.0