The Khinchin-Kahane inequality and Banach space embeddings for metric groups [article]

Apoorva Khare, Bala Rajaratnam
2016 arXiv   pre-print
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
more » ... ables with values in arbitrary abelian normed metric semigroups.
arXiv:1610.03037v1 fatcat:52kyekonmjgcjj4ivwmmxwwwzm