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Joel Moreira's math blogThu, 07 Jun 2018 00:52:42 +0000hourly1http://wordpress.com/Comment on Factors and joinings of measure preserving systems by Entropy of measure preserving systems | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2014/01/07/factors-and-joinings-of-measure-preserving-systems/#comment-1146
Thu, 07 Jun 2018 00:52:42 +0000http://joelmoreira.wordpress.com/?p=423#comment-1146[…] notion of isomorphism in the category of measure preserving systems (defined, for instance, in this earlier post) is fairly flexible, as it allows measure perturbations. For instance, the system where is the […]
]]>Comment on Ergodic Decomposition by Inaugural post: Three different entropies, variational principle and the degree formula. – That Can't Be Right
https://joelmoreira.wordpress.com/2013/09/20/ergodic-decomposition/#comment-1145
Mon, 04 Jun 2018 12:23:58 +0000http://joelmoreira.wordpress.com/?p=366#comment-1145[…] $mu in M(T,X)$ for which $T^{-1}A = A Rightarrow mu(A) in { 0, 1 }$. It relies on the ergodic decomposition theorem which I hope to cover in a subsequent […]
]]>Comment on Ergodic Decomposition by Three different entropies, variational principle and the degree formula. – Blog Tigle goes here
https://joelmoreira.wordpress.com/2013/09/20/ergodic-decomposition/#comment-1144
Tue, 29 May 2018 09:31:02 +0000http://joelmoreira.wordpress.com/?p=366#comment-1144[…] $mu in M(T,X)$ for which $T^{-1}A = A Rightarrow mu(A) in { 0, 1 }$. It relies on the ergodic decomposition theorem which we have not […]
]]>Comment on Disintegration of measures by Jc
https://joelmoreira.wordpress.com/2013/09/08/disintegration-of-measures/#comment-1143
Sun, 20 May 2018 07:11:31 +0000http://joelmoreira.wordpress.com/?p=360#comment-1143I’m wondering, sir- can one define a measure using disintegration of measure if one has a random variable X with measure \mu and a pushforward via f? In other words, if there is no uncertainty conditioned on X (or Dirac measure supported on f(X) if you will, can you rigorously constrict a measure via disintegration of measure? If so, how? I’ve been trying to figure this out with no avail.
]]>Comment on Sets of nice recurrence by Optimal intersectivity | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2013/03/04/323/#comment-1136
Thu, 26 Apr 2018 09:55:52 +0000http://joelmoreira.wordpress.com/?p=323#comment-1136[…] than being infinite . Something one can not hope for is that the set has positive density, as showed in my previous post, using Forest’s theorem that not all sets of recurrence are sets of nice […]
]]>Comment on Erdős Sumset conjecture by Optimal intersectivity | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2017/08/20/659/#comment-1135
Thu, 26 Apr 2018 09:55:44 +0000http://joelmoreira.wordpress.com/?p=659#comment-1135[…] intersectivity result of Bergelson, first used in this paper, and which I have mentioned before in this […]
]]>Comment on Recurrence theorems by Optimal intersectivity | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2012/04/15/recurrence-theorems/#comment-1134
Thu, 26 Apr 2018 09:55:41 +0000http://joelmoreira.wordpress.com/?p=229#comment-1134[…] is the following intersectivity result of Bergelson, first used in this paper, and which I have mentioned before in this […]
]]>Comment on Jin’s Theorem by A proof of the Erdős sumset conjecture | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2013/02/22/jins-theorem/#comment-1090
Sat, 03 Mar 2018 04:01:34 +0000http://joelmoreira.wordpress.com/?p=314#comment-1090[…] proof of Theorem 10 is inspired by an argument of Beiglböck described in my previous post. One can rephrase the statement of Beiglböck’s result as stating that for any sets one can […]
]]>Comment on The Ergodic Theorem by A proof of the Erdős sumset conjecture | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2013/01/17/the-ergodic-theorem/#comment-1089
Sat, 03 Mar 2018 04:01:31 +0000http://joelmoreira.wordpress.com/?p=305#comment-1089[…] of Besicovitch almost periodic functions by trigonometric polynomials, together with the pointwise ergodic theorem to obtain a similar […]
]]>Comment on Jacobs-de Leeuw-Glicksberg Decomposition by A proof of the Erdős sumset conjecture | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2012/05/11/koopman-von-neumann-decomposition/#comment-1088
Sat, 03 Mar 2018 04:01:28 +0000http://joelmoreira.wordpress.com/?p=242#comment-1088[…] definition is heavily influenced by the corresponding notion in ergodic theory (see, for instance Definition 1 in this previous […]
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