 Rademacher function

On $[0,1)$ with Lebesgue measure, the functions $r_n(t)=(-1{)}^{\lfloor 2^{n}t\rfloor }$, $n\ge 1$, are independent symmetric Rademacher random variables. Every prescribed pattern for the first $n$ functions occupies a dyadic interval of measure $2^{-n}$. Their closed span in $L^1$ is isomorphic to the l2 sequence space by the Khintchine inequality.