Dyadic partition
= Dyadic partition
{title2=$I_{J,k}=[k2^{-J},(k+1)2^{-J})$}
A <dyadic partition> of $[0,1]$ at level $J$ consists of $2^J$ equal cells of length $2^{-J}$. Each cell splits into two cells at the next level. Use left-closed, right-open cells, adding the endpoint $1$ to the final cell when a pointwise representative is needed. These nested partitions underlie the <Haar scaling functions> and <Haar wavelets>.