"Khinchine’s Inequalities.”

Abstract: 

     The Rademacher functions r_n on the interval
[0,1] are a sequence of {1, -1}-valued stochastically independent, identically distributed (i.i.d.)
random variables. They span a Banach subspace of L^2[0,1] that is a copy of the Hilbert sequence space ell^2.

        This is also true for any p with 1 <= p < infinity : The Rademacher sequence (r_n)_n
spans a Banach subspace of the Lebesgue function space L^p[0,1] that is an isomorphic copy of ell^2.

         This interesting classical Banach space fact follows from Khinchine’s Inequalities, that we will discuss and prove.