Journal of the
Korean Mathematical Society JKMS

The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to $\left({0,\infty } \right)$ instead of $\left( {0,2} \right)$, we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.

Keywords: conditional independence, conditionally identical distributiveness, conditional median, conditional symmetrization inequality, conditional Kahane-Hoffmann-J{\o}rgensen inequality

MSC numbers: 60F15, 60E15