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 probability distribution>[symmetric] <Rademacher random variables>. Every prescribed pattern for the first $n$ <functions> occupies a <dyadic interval> of measure $2^{-n}$. Their <closed linear span>[closed span] in $L^1$ is isomorphic to the <l2 sequence space> by the <Khintchine inequality>.