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The Levy-Ito decomposition of sample paths of Levy processes with values in the space of probability measures

. A deﬁnition of L´evy processes with values in the space of probability measures was introduced by Shiga and Tanaka (Electronic J. Prob. 11 (2006)). It is shown that the L´evy process with values in the space of probability measures in law has a modiﬁcation satisfying a certain condition. The modiﬁcation is a L´evy process in the sense of Shiga and Tanaka. The L´evy-Itˆo decomposition of sample paths of the L´evy process satisfying the condition is derived.