Marcinkiewicz-type Strong Law of Large Numbers for Double Arrays of Pairwise Independent Random Variables
نویسندگان
چکیده
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 ∑m i=1 ∑n j=1 ( Xij−EXij ) (mn)1/p → 0 a.s. as m∨n →∞. (0.1) Under the weak condition of E|X|p log+ |X| <∞, it converges to 0 in L1. And the results can be generalized to an r -dimensional array of random variables under the conditions E|X|p( log+ |X|)r+1 <∞, E|X|p( log+ |X|)r−1 <∞, respectively, thus, extending Choi and Sung’s result [1] of the one-dimensional case.
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