Abstract:The Plünnecke-Ruzsa inequality is a fundamental tool to control the growth of finite subsets of abelian groups under repeated addition and subtraction. Other tools to handle sumsets have gained applicability by being extended to more general subsets of more general groups. This motivates extending the Plünnecke-Ruzsa inequality, in particular to measurable subsets of compact abelian groups by replacing the cardinality with the Haar probability measure. This objective is related to the question of the stability… Show more
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