Silva, João Lita da2025-06-182025-10-150022-247XPURE: 117438788PURE UUID: e9f42bc4-4b3b-481c-be90-7ca583912014Scopus: 105004315033http://hdl.handle.net/10362/184231Funding Information: This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of project UIDB/04035/2020 (GeoBioTec). Publisher Copyright: © 2025 Elsevier Inc.Given a sequence {Xn,n⩾1} of independent and identically distributed random variables such that E|X1|p<∞ for some 1<p<2, and a triangular array {an,j,1⩽j⩽n,n⩾1} of real numbers monotonic with respect to one of the indices satisfying max1⩽j⩽n⁡|an,j|=O(1), n→∞, it is shown that n−1/p∑j=1nan,j(Xj−EXj)⟶a.s.0.9166309engIndependent and identically distributed random variablesStrong law of large numbersWeighted sumsAnalysisApplied Mathematicsjournal article10.1016/j.jmaa.2025.129618https://www.scopus.com/pages/publications/105004315033