Title Trimmed sums for observables on the doubling map Tanja Schindler (Australian National University) Tanja Schindler Dynamical Systems and Fluid Dynamics 14:30:00 2017-09-25 For measure preserving ergodic dynamical systems there is no strong law of large numbers if the expectation has infinite mean. In some cases it is possible to obtain a generalised strong law of large numbers by deleting the maximum entry, for examples for the digits of a continued fraction expansion. Haynes proved that there is no strong law of large numbers by only deleting a finite number of terms (light trimming) on iterations of the doubling map with observable $1/x$, eventhough this would be possible if one considered independent random variables with the same distribution function. Based on this result Haynes and myself have shown that a strong law does still hold in this case depending if for the number of deleted terms $b_n$ of the sum of the first $n$ entries it holds that $\lim_{n\to\infty}b_n/\log\log\log n=\infty$ or not.