P-asymptotically Equivalent in Probability
DOI:
https://doi.org/10.5644/SJM.06.2.06Keywords:
P-convergent, P-asymptotical equivalent regular in probabilityAbstract
In this paper we present the following definitions P-asymptotically equivalent probability of multiple $L$ and P-asymptotically probability regular. In addition to these definitions we asked and provide answers for the following questions.
(1)If $x\stackrel{Probability}{\approx} y$ then what type of four dimensional matrices transformation will satisfy the following $\mu (Ax)\stackrel{Probability}{\approx} \mu (Ay)$?
(2) If $[x]$ and $[y]$ are bounded double sequences that P-asymptotically converges at the same rate, then what are the necessary and sufficient conditions on the entries of any four dimensional matrix transformation $A$ that will ensure that $A$ sums $[x]$ and $[y]$ at the same P-asymptotic rate?
(3) What are the conditions on the entries of four dimensional matrices that ensure the preservation of P-asymptotically convergence in probability?
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