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YCor
YCor
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The space of ergodic elements of a tolpologicaltopological or Lie group

Let $G$ be a compact topological group with normalized Haar measure $\mu$. An element $g\in G$ is an ergodic element if the mapping $L_g:G \to G $ with $x\mapsto gx$ is an ergodic map.The The set of ergodic elements of a group $G$ is denoted by $E(G)$

Is there a compact topological group or a compact Lie group for which the set of all ergodic elements have intermediate measuare measure namely we have $0<\mu(E(G)<1$?

The space of ergodic elements of a tolpological or Lie group

Let $G$ be a compact topological group with normalized Haar measure $\mu$. An element $g\in G$ is an ergodic element if the mapping $L_g:G \to G $ with $x\mapsto gx$ is an ergodic map.The set of ergodic elements of a group $G$ is denoted by $E(G)$

Is there a compact topological group or a compact Lie group for which the set of all ergodic elements have intermediate measuare namely we have $0<\mu(E(G)<1$?

The space of ergodic elements of a topological or Lie group

Let $G$ be a compact topological group with normalized Haar measure $\mu$. An element $g\in G$ is an ergodic element if the mapping $L_g:G \to G $ with $x\mapsto gx$ is an ergodic map. The set of ergodic elements of a group $G$ is denoted by $E(G)$

Is there a compact topological group or a compact Lie group for which the set of all ergodic elements have intermediate measure namely we have $0<\mu(E(G)<1$?

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Ali Taghavi
Ali Taghavi
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The space of ergodic elements of a tolpological or Lie group

Let $G$ be a compact topological group with normalized Haar measure $\mu$. An element $g\in G$ is an ergodic element if the mapping $L_g:G \to G $ with $x\mapsto gx$ is an ergodic map.The set of ergodic elements of a group $G$ is denoted by $E(G)$

Is there a compact topological group or a compact Lie group for which the set of all ergodic elements have intermediate measuare namely we have $0<\mu(E(G)<1$?