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Joel Moreira's math blogSat, 03 Mar 2018 04:01:34 +0000hourly1http://wordpress.com/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 […]
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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 […]
]]>Comment on Properties of ultrafilters and a Theorem on arithmetic combinatorics by A proof of the Erdős sumset conjecture | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2012/11/14/properties-of-ultrafilters-and-a-theorem-of-hindman-on-arithmetic-combinatorics/#comment-1087
Sat, 03 Mar 2018 04:01:24 +0000http://joelmoreira.wordpress.com/?p=283#comment-1087[…] To overcome this issue we make use of the notion of ultrafilters. An ultrafilter is a collection of subsets of which is closed under finite intersections and has the properties that if and , then ; and if , then . One should think of ultrafilters in this context as elements of the Stone-Čech compactification of , so that is a discrete but dense subset of . Given a set and an ultrafilter , we denote by the set . One can interpret as a generalized shift of , which has some, but not all, properties of “principal” shifts with . For more background on ultrafilters, see also this previous post. […]
]]>Comment on Weak Mixing by A proof of the Erdős sumset conjecture | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2013/02/11/weak-mixing/#comment-1086
Sat, 03 Mar 2018 04:01:21 +0000http://joelmoreira.wordpress.com/?p=308#comment-1086[…] theory that weak mixing and almost periodicity are extreme points of a dichotomy (see for instance, this post) and so it was natural to try to patch these two observations into a proof of Theorem 2 in general. […]
]]>Comment on Erdős Sumset conjecture by A proof of the Erdős sumset conjecture | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2017/08/20/659/#comment-1085
Sat, 03 Mar 2018 04:01:15 +0000http://joelmoreira.wordpress.com/?p=659#comment-1085[…] Florian Richter, Donald Robertson and I have uploaded to the arXiv our paper entitled A proof of the Erdős sumset conjecture. The main goal of the paper is to prove the following theorem, which verifies a conjecture of Erdős discussed in this previous post. […]
]]>Comment on Measure preserving actions of affine semigroups and {x+y,xy} patterns by merniu
https://joelmoreira.wordpress.com/2015/10/12/measure-preserving-actions-of-affine-semigroups-and-xyxy-patterns/#comment-1060
Mon, 08 Jan 2018 18:55:35 +0000http://joelmoreira.wordpress.com/?p=620#comment-1060an application are suggested for some operator as Lagrangian as say prof dr mircea orasanu and prof horia orasanu
]]>Comment on Measure preserving actions of affine semigroups and {x+y,xy} patterns by merniu
https://joelmoreira.wordpress.com/2015/10/12/measure-preserving-actions-of-affine-semigroups-and-xyxy-patterns/#comment-1059
Mon, 08 Jan 2018 18:53:44 +0000http://joelmoreira.wordpress.com/?p=620#comment-1059indeed are very important these as say prof dr mircea orasanu and prof horia orasanu
]]>Comment on Weighted densities with multiplicative structure by Single and multiple recurrence along non-polynomial sequences | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2014/11/14/weighted-densities-and-multiplicative-structure/#comment-1020
Sat, 18 Nov 2017 20:14:18 +0000http://joelmoreira.wordpress.com/?p=532#comment-1020[…] distribution. Instead we resort to the concept of Riesz means (or weighted means, as discussed in this previous post), and indeed of uniform Riesz […]
]]>Comment on Piecewise syndetic sets, topological dynamics and ultrafilters by Single and multiple recurrence along non-polynomial sequences | I Can't Believe It's Not Random!
https://joelmoreira.wordpress.com/2016/04/18/piecewise-syndetic-sets-topological-dynamics-and-ultrafilters/#comment-1019
Sat, 18 Nov 2017 20:14:13 +0000http://joelmoreira.wordpress.com/?p=627#comment-1019[…] in the sense that a set is thick if and only if its complement is not syndetic and vice-versa. See my previous post for some discussion of the basic properties of thick and syndetic […]
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