Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that

(i) | $E, F_1, \ldots, F_N \in \mathcal{F}$ are each a D1109: Measurable set in $M$ |

(ii) | $F_1, \ldots, F_N$ is a D5143: Set partition of $X$ |

This result is a particular case of R3645: Countable partition additivity of unsigned basic measure. $\square$