If $T:[0,1] rightarrow [0,1]$ preserves Lebesgue, then $liminf_n(n|T^n(x)-x|) leq 1$ [closed]

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Let $T:[0,1] rightarrow [0,1]$ be a measurable function such that $T$ preserves Lebesgue, then for almost all point:



$$liminf_n(n|T^n(x)-x|) leq 1$$










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closed as off-topic by user99914, zhoraster, Jendrik Stelzner, heropup, Xander Henderson Sep 7 at 1:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, zhoraster, Jendrik Stelzner, heropup, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.












  • why is the the $liminf $ at most 1?
    – cactus314
    Sep 6 at 11:45














up vote
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down vote

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Let $T:[0,1] rightarrow [0,1]$ be a measurable function such that $T$ preserves Lebesgue, then for almost all point:



$$liminf_n(n|T^n(x)-x|) leq 1$$










share|cite|improve this question















closed as off-topic by user99914, zhoraster, Jendrik Stelzner, heropup, Xander Henderson Sep 7 at 1:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, zhoraster, Jendrik Stelzner, heropup, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.












  • why is the the $liminf $ at most 1?
    – cactus314
    Sep 6 at 11:45












up vote
3
down vote

favorite
3









up vote
3
down vote

favorite
3






3





Let $T:[0,1] rightarrow [0,1]$ be a measurable function such that $T$ preserves Lebesgue, then for almost all point:



$$liminf_n(n|T^n(x)-x|) leq 1$$










share|cite|improve this question















Let $T:[0,1] rightarrow [0,1]$ be a measurable function such that $T$ preserves Lebesgue, then for almost all point:



$$liminf_n(n|T^n(x)-x|) leq 1$$







measure-theory lebesgue-measure ergodic-theory






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share|cite|improve this question













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edited Sep 6 at 10:55









Jendrik Stelzner

7,69121137




7,69121137










asked Sep 6 at 2:45









Santiago Radi

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312




closed as off-topic by user99914, zhoraster, Jendrik Stelzner, heropup, Xander Henderson Sep 7 at 1:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, zhoraster, Jendrik Stelzner, heropup, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by user99914, zhoraster, Jendrik Stelzner, heropup, Xander Henderson Sep 7 at 1:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, zhoraster, Jendrik Stelzner, heropup, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.











  • why is the the $liminf $ at most 1?
    – cactus314
    Sep 6 at 11:45
















  • why is the the $liminf $ at most 1?
    – cactus314
    Sep 6 at 11:45















why is the the $liminf $ at most 1?
– cactus314
Sep 6 at 11:45




why is the the $liminf $ at most 1?
– cactus314
Sep 6 at 11:45















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