关于空隙律/继承律大数定律的必要和充分条件
Necessary and Sufficient Conditions for the Lacunary/Hereditary Laws of Large Numbers
AI总结：
本文研究了空隙律和继承律大数定律的必要和充分条件，提出更弱的Egorov型条件，并解决了可交换序列中弱大数定律的问题。
摘要：
Komlos著名的定理指出，L1有界性是给定函数序列中存在一个子序列（以“空隙”方式）以及其每一个进一步的子序列（“继承性”）都满足强大数定律的充分条件。本文在此背景下识别出略弱的Egorov型条件，不仅在该情境下是充分的，而且也是必要的。此外，还为一般序列的空隙/继承版弱大数定律以及可交换序列中的弱大数定律发展了必要和充分条件，这些都是长期未解决的问题。
英文摘要：
The celebrated theorem of Komlos asserts that L1-boundedness is sufficient for a given sequence of functions to contain a subsequence along which (in a "lacunary" manner), and along whose every further subsequence ("hereditarily"), a strong law of large numbers holds. We identify here slightly weaker, Egorov-type conditions, as not only sufficient in this context, but necessary as well. Necessary and sufficient conditions are developed also for the lacunary/hereditary version of the weak law of large numbers for general sequences, as well as for the weak law of large numbers in the context of exchangeable sequences, both long-open questions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
