The Marcinkiewicz-Zygmund law of large numbers for exchangeable arrays

We show a Marcinkiewicz-Zygmund law of large numbers for jointly and dissociated exchangeable arrays. The result holds both in $L^r$ ($r\in (0,2)$) and almost surely. As a result, we obtain a law of iterated logarithm for such arrays under a weaker moment condition than the existing one.