Abstract
Isoperimetric inequalities are used to obtain measure estimates on almost constancy sets of functions on product spaces. These are applied to produce almost unconditional or symmetric block sequences from given sequences. Their length, which is (logn)1/2 in the general case, improves ton a where a cotype condition is imposed or when the given sequences arep-type attaining for somep<2. In thep-type attaining case, block sequences (1+e)-equivalent to the unit vector basis ofl p m can be obtained when log logm ∼ log logn.
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