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g-extension

Ergodic Theory and Dynamical Systems (1)

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Conditional mean dimension
Part of
- Spaces with richer structures
BINGBING LIANG
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 10 / October 2022

Published online by Cambridge University Press:

06 September 2021, pp. 3152-3166

Print publication:

October 2022
- Article
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We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an extension system. The conditional mean dimension for G-extensions is computed. We also exhibit some applications in dynamical embedding problems.