On the Kolmogorov-Feller weak law of large numbers for the Fréchet mean on non-compact symmetric spaces

We prove the Kolmogorov-Feller weak law of large numbers for sample Fréchet means on non-compact symmetric spaces. The result covers independent, non-identically distributed data, extending beyond the i.i.d. setting. Examples of symmetric positive-definite matrices and product symmetric spaces are provided.