1 Correction to: Ann. Henri Poincaré 22, Issue 5 (2021) https://doi.org/10.1007/s00023-020-01014-z

Claims (a) and (b) in Chernoff’s theorem quoted in Sect. 3 contain misprints; the correct text reads:

(a) For some \(\lambda _0>0\), the family \(\big \{\big (\lambda _0 I + \tfrac{I-F(\varepsilon )}{\varepsilon }\big )^{-1}\big \}_{\varepsilon >0}\) converges strongly to \((\lambda _0 I+A)^{-1}\) as \(\varepsilon \rightarrow 0+\).

(b) As \(n\rightarrow \infty \), \(\{F(\tfrac{t}{n})^n\}_{n=1}^{\infty }\) converges strongly to \(\mathrm {e}^{-tA}\), uniformly on bounded t-intervals.