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A pointwise ergodic theorem for Fuchsian groups

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Figure

Fig. 1. Labelling the sides of the fundamental domain R. The label e appears interior to R on the side ofadjacent to the region e−1R.
Fig. 2. Intervals round a vertex vlevels 2intervals except those of level 0 and 1 are contained in of R
Fig. 3. Intervals subtended by a side of Rtop level intervals at either end ofwhich is contained in neither
Fig. 4. Consecutive cycles.

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