  We establish a strong law of large numbers under intermediate trimming for a
particular example of Birkhoff sums of a non-integrable observable over the
doubling map. It has been shown in a previous work by Haynes that there is no
strong law of large numbers for the considered system after removing finitely
many summands (light trimming) even though i.i.d. random variables and also
some dynamical systems with the same distribution function obey a strong law of
large numbers after removing only the largest summand.
