Abstract
AbstractWe prove the first orbit equivalence superrigidity results for actions of type III$_\unicode{x3bb} $when$\unicode{x3bb} \neq 1$. These actions arise as skew products of actions of dense subgroups of$\operatorname {SL}(n,\mathbb {R})$on the sphere$S^{n-1}$and they can have any prescribed associated flow.
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