Question

Definition. Let v be a probability measure on (R, B(R)). The probabil-ity measure v is called infinitely divisible if for any n € N, n ≥ 2, there exists a probability measure Vn on (R, B(R)) such that \nu_{n}^{* n}=\nu Here \nu_{n}^{* n}:=\underbrace{\nu_{n} * \nu_{n} * \cdots * \nu_{n}}_{n \text { times }} Problem. Let (µt)t>o be a convolution semigroups of probability measures on (R, B(R)). Prove that, for each t > 0, the probability measure ut is infinitely divisible.

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