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Equicontinuity and Convergent Sequences in the Spaces O<sup>\</sup>prime<sub>C</sub>and O<sub>M</sub>
Characterizations of equicontinuity and convergent sequences are given for the space $\mathcal O^\prime_C(\mathbb R^n)$ of rapidly decreasing distributions and the space $\mathcal O_M(\mathbb R^n)$ of slowly increasing infinitely differentiable functions.