Manuscript Em06-B@1 · Em06-B-v1.tex · section · 61e38859

Metric, switch, and observation-test changes

Quantitative stability of the classical inputs › Metric, switch, and observation-test changes · lines 1224–1236

Em06-B@1#eq:symbol-stability

Let $z_{0}, z_{1} \in S$ and $o_{a} = 2 Re ⟨ v_{a}, z_{a} ⟩$ . Then

∣ o_{1} - o_{0} ∣ \leq 2∥ v_{1} - v_{0} ∥∥ z_{1} ∥ + 2∥ v_{0} ∥∥ z_{1} - z_{0} ∥.

Thus the preparation topology is explicitly the Hilbert norm, even though smooth amplitudes are used to name classical fields.

Displayed formulas in this passage

Em06-B@1#eq:symbol-stability · line 1228
$∣ o_{1} - o_{0} ∣ \leq 2∥ v_{1} - v_{0} ∥∥ z_{1} ∥ + 2∥ v_{0} ∥∥ z_{1} - z_{0} ∥.$