Thursday, December 6, 2018 - 16:00 to 17:00

321 Thackeray

### Abstract or Additional Information

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.