## Abstract

This note corrects an error in [1], Lemma 3.7. The lemma is not correct as stated, and the first conclusion must instead be stated as a hypothesis. This erratum corrects the statement of the lemma and then shows that the additional hypothesis is satisfied in each of the three applications of the lemma later in the paper. The main results of the paper remain unchanged. The error in [1], Lemma 3.7, is at the end of the “first step” of the proof. Specifically, the last equation before the “second step” (lines 5–6 of page 3769) is not accurate, because the preceding equation was proven only for all Fμ t -measurable functions φ1(μ), not for all Fμ T -measurable functions. We rewrite the lemma as follows, stating equivalence between its two claims as well as a third and often more convenient form.

Original language | English (US) |
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Pages (from-to) | 2644-2646 |

Number of pages | 3 |

Journal | Annals of Probability |

Volume | 48 |

Issue number | 5 |

DOIs | |

State | Published - Sep 2020 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Keywords

- Mckean–vlasov equations
- Mean field games
- Relaxed controls
- Stochastic optimal control
- Weak solutions