The Khinchin–kahane Inequality and Banach Space Embeddings for Metric Groups
نویسنده
چکیده
We extend the Khinchin–Kahane inequality to an arbitrary abelian metric group G . In the special case where G is normed, we prove a refinement which is sharp and which extends the sharp version for Banach spaces. We also provide an alternate proof for normed metric groups as a consequence of a general “transfer principle”. This transfer principle has immediate applications to stochastic inequalities for G -valued random variables. We also show how to use it to define the expectation of random variables with values in arbitrary abelian normed metric semigroups.
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