On the ($$\boldsymbol{p,q}$$)-Type Strong Law of Large Numbers for Sequences of Pairwise Independent Random Vectors in Hilbert Spaces

The $$(p,q)$$ -type strong law of large numbers was studied by Li, Qi, and Rosalsky (Trans. Amer. Math. Soc., 2016) and Thành (Math. Nachr., 2023) for independent Banach space-valued random elements. This paper provides sufficient conditions for the $$(p,q)$$ -type strong law of large numbers for sequences of pairwise independent random vectors in Hilbert spaces. Although we assume only pairwise independence rather than mutual independence of the underlying random vectors, the sufficient conditions are only slightly stronger than those in the aforementioned works.