What did you try? The documentation may lack examples written out for you, but it documents the relevant functions.
For example, this code applies your filter 1 element at a time:
butterF = DSP.Filters.DF2TFilter(butter)
results2 = zeros(N)
for i = 1:N
@views filt!(results2[i:i], butterF, measurements[i:i])
end
(Bigger batches should be more efficient, but the complexity should still be linear in N.)