Summary
We give a simpler proof of the probability invariance principle for triangular arrays of independent identically distributed random variables with values in a separable Banach space, recently proved by de Acosta [1], and improve this result to an almost sure invariance principle.
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Dabrowski, A., Dehling, H. & Philipp, W. An almost sure invariance principle for triangular arrays of banach space valued random variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 483–491 (1984). https://doi.org/10.1007/BF00531835
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DOI: https://doi.org/10.1007/BF00531835