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| 摘要: |
| 本文研究在局部连通图中取值的随机元的r-阶均值集、r-阶广义样本均值集的基本性质及其极限性质.利用关于随机元的分离引理以及随机游动的常返性，得到了关于图值随机元序列广义强大数定理.推广了已有的结果. |
| 关键词: 强大数定律 图 r-阶权函数 r-阶均值集 r-阶广义样本均值 随机游动 |
| DOI： |
| 分类号:O211.4 |
| 基金项目:国家自然科学基金（11071104）；国家社会科学基金（13BJY011）；安徽省自然科学基金（1308085QF113；1408085MA04）；安徽工业大学研究生创新基金（2012090）资助. |
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| ON SOME LIMIT THEOREMS FOR GRAPH-VALUED RANDOM ELEMENTS |
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WANG Zhong-zhi,LI Wen-xi
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| Abstract: |
| In this paper, the authors discuss the basic properties of the general rth order mean set and rth order sample mean set of random elements, which take values on a locally connected graph, and the limit properties of them. By applying the separation lemma of random elements and the recurrence of random walk, we obtain the general strong law of large numbers for graph-valued random elements. Moreover, we generalize the existing results. |
| Key words: general strong law of large numbers graph r-thorder weight function r-thorder mean set r-thorder sample mean set random walk |
