Unconditional and symmetric sets in n-dimensional normed spaces

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 (log n)^1/2 in the general case, improves to n ^a where a cotype condition is imposed or when the given sequences are p-type attaining for some p<2. In the p-type attaining case, block sequences (1+ε)-equivalent to the unit vector basis of l _p ^m can be obtained when log log m ∼ log log n.