{"docId":10292,"paperId":10292,"url":"https:\/\/cm.episciences.org\/10292","doi":"10.46298\/cm.10292","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":673,"name":"Volume 31 (2023), Issue 1"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03842221","repositoryVersion":2,"repositoryLink":"https:\/\/hal.science\/hal-03842221v2","dateSubmitted":"2022-11-10 14:40:03","dateAccepted":"2022-11-10 18:13:01","datePublished":"2022-11-21 17:10:32","titles":{"en":"A General Weak Law of Large Numbers for Sequences of $L^{p}$ Random Variables"},"authors":["Chou, Yu-Lin"],"abstracts":{"en":"Without imposing any conditions on dependence structure, we give a seemingly overlooked simple sufficient condition for $L^{p}$ random variables $X_{1}, X_{2}, \\dots$ with given $1 \\leq p \\leq +\\infty$ to satisfy \\[\\frac{1}{a_{n}}\\sum_{i=1}^{b_{n}}(X_{i} - \\mathbb{E} X_{i}) \\overset{L^{p}}\\to 0 \\,\\,\\, \\mathrm{as}\\, n \\to \\infty,\\]where $(a_{n})_{n \\in \\mathbb{N}}, (b_{n})_{n \\in \\mathbb{N}}$ are prespecified unbounded sequences of positive integers.Some unexpected convergences of sample means follow."},"keywords":[["convergence in probability"],["$L^{p}$-convergence"],["laws of large numbers"],"[MATH]Mathematics [math]"]}