Summary
The Prohorov law of large numbers is extended to random variables taking their values in a 2-uniformly smooth Banach space (B, ∥ ∥). In our result the classical assumption of the scalar case is replaced by the following one:
where:
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Heinkel, B. Une extension de la loi des grands nombres de Prohorov. Z. Wahrscheinlichkeitstheorie verw Gebiete 67, 349–362 (1984). https://doi.org/10.1007/BF00535009
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DOI: https://doi.org/10.1007/BF00535009