Dynamics via measurability
<p>Generators <mml:math alttext="$f$"> <mml:mi>f</mml:mi> </mml:math> for <mml:math alttext="$sigma$"> <mml:mi>σ</mml:mi> </mml:math>-algebras can be used to vie...
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| Format: | Article |
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| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/81356 |
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| Summary: | <p>Generators <mml:math alttext="$f$"> <mml:mi>f</mml:mi> </mml:math> for <mml:math alttext="$sigma$"> <mml:mi>σ</mml:mi> </mml:math>-algebras can be used to view the dynamics of an invertible measurable transformation <mml:math alttext="$T$"> <mml:mi>T</mml:mi> </mml:math> in terms of the range values of <mml:math alttext="$fcirc T$"> <mml:mi>f</mml:mi> <mml:mo>∘</mml:mo> <mml:mi>T</mml:mi> </mml:math>. Such generators are the norm rather than the exception. Related measurable and quantitative methods of estimating a function from the behavior of ergodic averages are also discussed.</p> |
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| ISSN: | 1085-3375 |