Manuscript Oai280-B@1 · Oai280-B.tex · section · 6d92ab75

The connected simultaneous theorem

Bell correlations and simultaneous finite-data certification › The connected simultaneous theorem · lines 1383–1407

Oai280-B@1#eq:statistics, Oai280-B@1#eq:intervals

Define

c_{A j} r_{A j} F_{A} = \frac{1}{n _{A j}} i \sum Z_{A j i}, = \frac{2}{n _{A j}} lo g \frac{6 K}{α _{s}}, R_{A} = \frac{r _{A x} + r _{A y} + r _{A z}}{4}, = \frac{1 + c _{A x} - c _{A y} + c _{A z}}{4} .

Set $[u]_{[0, 1]} = max {0, min {1, u}}$ , and put

F_{L, A} F_{U, A} L_{A} U_{A} = [F_{A} - R_{A} - b_{cal, A}]_{[0, 1]}, = [F_{A} + R_{A} + b_{cal, A}]_{[0, 1]}, = max {0, 1 - F_{U, A} - b_{A}}, = min {1, 2 1 - F_{L, A} + b_{A}} .

Displayed formulas in this passage

Oai280-B@1#eq:statistics · line 1386
$c_{A j} r_{A j} F_{A} = \frac{1}{n _{A j}} i \sum Z_{A j i}, = \frac{2}{n _{A j}} lo g \frac{6 K}{α _{s}}, R_{A} = \frac{r _{A x} + r _{A y} + r _{A z}}{4}, = \frac{1 + c _{A x} - c _{A y} + c _{A z}}{4} .$
Oai280-B@1#eq:intervals · line 1398
$F_{L, A} F_{U, A} L_{A} U_{A} = [F_{A} - R_{A} - b_{cal, A}]_{[0, 1]}, = [F_{A} + R_{A} + b_{cal, A}]_{[0, 1]}, = max {0, 1 - F_{U, A} - b_{A}}, = min {1, 2 1 - F_{L, A} + b_{A}} .$