will be characterized by a probability distribution $\phi:\:{\mathbb{R}}_+ \to{\mathbb{R}}_+$, which is typically a bounded, compactly supported function – in a precisely posed experiment it is sharply peaked, of course. Corollary \[cor1\] then gives $$\int \phi(t)\, \left\|\,[P\exp(-i\varepsilon tH/n) P]^n f -
  \exp(-i\varepsilon tH_P)\,P f \right\|^2\,dt \to 0 \label{physZeno}$$ as $n\to\infty$, in other words, the Zeno dynamics limit is valid after averaging over experimental errors, however small they are.]{}

[While the proof of strong convergence in ${\cal H}$ in Theorem \[main\] and Corollaries \[cor1\] and \[cor2\] remains elusive without the finite-dimension assumption, such a claim can be easily established in the orthogonal complement of the subspace $P{{\mathcal H}}$. Indeed, taking $f\in Q{\cal H}$, where $Q:=I-P$, we have $$\begin{aligned}
 (P(1/n)e^{-i\varepsilon tH/n} P(1/n))^n f
  &\!=\!& (P(1/n)e^{-i\varepsilon tH/n} P(1/n))^n P(1/n)Qf\,,\\
 (e^{-i\varepsilon tH/n} P(1/n))^n f
 &\!=\!& (e^{-i\varepsilon tH/n} P(1/n))^n P(1/n)Qf\,,\end{aligned}$$ which converge to zero, uniformly on each compact $t$-interval in ${\mathbb{R}}$, as $n\rightarrow \infty$, because $P(\tau)
\stackrel{\scriptsize{s}}{\rightarrow} P$ as $\tau \rightarrow 0$. This gives the result for (\[ae:product-s\]) and (\[ae:product-ns2\]), while for (\[ae:product-ns\]) one has to employ in addition the relation (\[diff:ns-s\]) below. ]{}

[The fact that the product formulae require $H_P$ to be densely defined is nontrivial. Recall the example of [@Ex Rem. 2.4.9] in 