Are those dyadic intervals? I see that those are not Dyadic intervals because the length of the dyadic interval must be $2^{-j}$, am I right? or can the length of the dyadic interval be different from this? $$I_{R} = [(2k+1)2^{-j-1},(k+1)2^{-j}[, I_{L} = [k 2^{-j},(2k+1)2^{-j-1}[$$ If they are Dyadic intervals what are their lengths?

$$(k+1)2^{-j}-(2k+1)2^{-j-1}=2^{-j-1}$$ and

$$(2k+1)2^{-j-1}-k2^{-j}=2^{-j-1},$$

so these are indeed dyadic intervals.