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We establish a strong law of large numbers under intermediate trimming for aparticular example of Birkhoff sums of a non-integrable observable over thedoubling map. It has been shown in a previous work by Haynes that there is nostrong law of large numbers for the considered system after removing finitelymany summands (light trimming) even though i.i.d. random variables and alsosome dynamical systems with the same distribution function obey a strong law oflarge numbers after removing only the largest summand.

Trimmed sums for observables on the doubling map