Rademacher function
= Rademacher function
{c}
{title2=$r_n(t)=(-1)^{\lfloor2^nt\rfloor}$}
On $[0,1)$ with Lebesgue measure, the functions $r_n(t)=(-1)^{\lfloor2^nt\rfloor}$, $n\ge1$, 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>.