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Bulletin of the London Mathematical Society (1)

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INVARIANT SUBSETS AND INVARIANT MEASURES FOR IRREDUCIBLE ACTIONS ON ZERO-DIMENSIONAL GROUPS
MANFRED EINSIEDLER
Journal:

Bulletin of the London Mathematical Society / Volume 36 / Issue 3 / May 2004

Published online by Cambridge University Press:

28 April 2004, pp. 321-331

Print publication:

May 2004
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Algebraic higher-rank actions on connected groups are often remarkably rigid in their topological and measurable structure. In contrast to this, the author of this paper constructs uncountably many closed invariant sets and uncountably many invariant measures with positive entropy for irreducible algebraic ${\mathbb{Z}^d}$-actions on zero-dimensional groups.