Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables
Let {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn|≥t}≤P{|X|≥t} for all nonnegative real numbers t and E|X|p(log+|X|)3<∞, for 1<p<2, then we prove that ∑i=1m∑j=1n(Xij−EXij)(mn)1/p→0 a.s. as m∨n→∞. (0.1) Under the weak...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171299221710 |