发表机构
Óbuda University; Corvinus University of Budapest; University of Szeged（欧贝达大学; 布达佩斯科维努斯大学; 塞格德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文延续算子平均的强大数定律推广研究，澄清Thompson度量空间中相关强大数定律的错误，将矩条件放宽至$L/log^+(L)$并证明隐式随机逼近的几乎必然收敛。
AI 中文摘要
本文延续了作者在前期论文《广义算子平均的强大数定律》（Adv. Math. 457 (2024), 109933）中启动的、将强大数定律推广到算子平均的研究。特别地，我们澄清了Thompson度量空间中与一致指数收缩流相关的平均的强大数定律的陈述与证明中的一处错误；随后，我们通过证明单调算子在矩条件为$L/log^+(L)$下的隐式随机逼近的几乎必然收敛，将前述论文中算子平均的该强大数定律变体的限制性矩条件大幅放宽。
英文摘要
In this paper we continue the investigation of generalizations of the strong law of large numbers to operator means which has been initiated in the earlier paper "Strong law of large numbers for generalized operator means", Adv. Math. 457 (2024), 109933 of the authors. In particular, we clarify an inaccuracy in the statement and proof of the strong law for means associated with uniformly exponentially contracting flows in Thompson metric spaces. We then significantly improve the variant of this strong law given in the mentioned paper for operator means by relaxing the restrictive required moment condition to $L\log^+(L)$ by proving almost sure convergence of implicit stochastic approximations for monotone operators under this condition.
