For geodesically symmetric heavy-tailed distributions on non-compact symmetric spaces, the sample Fréchet mean converges in probability to the center of symmetry under the Kolmogorov-Feller tail condition.
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On the Kolmogorov-Feller weak law of large numbers for the Fr\'echet mean on non-compact symmetric spaces
For geodesically symmetric heavy-tailed distributions on non-compact symmetric spaces, the sample Fréchet mean converges in probability to the center of symmetry under the Kolmogorov-Feller tail condition.