Invariant Measure/Examples/Arcs on Unit Circle
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Example of Invariant Measure
Let $\CC$ denote the unit circle embedded in the complex plane:
- $\CC = \set {z \in \C: \cmod z = 1}$
The standard measure for arcs on $\CC$ is invariant under the mapping $\map T z = z^2$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): invariant measure
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): invariant measure