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Consider the ##CHSH=AB-AB'+A'B+A'B'##

Then the theorem states : ##-2\leq CHSH\leq 2##

Implying ##|<CHSH>|\leq 2##.

We could repeat the average : ##\langle |\langle CHSH\rangle|\rangle\leq 2##

Now Bell's theorem deals with large numbers average, in order to get 2 if we suppose a different variable for each covariance : ##A(\lambda_1)B(\lambda_1)-A(\lambda_2)B(\lambda_2)+A'(\lambda_3)B(\lambda_3)+A'(\lambda_4)B'(\lambda_4)##

Could we do a small number average for the interior average and a large number for exterior average. (In fact this gives the average of the absolute value) ?

For example the interior average could be about 1 value (number of photons per measurment, or maybe number of worlds ?) and the exterior a large number, giving : ##\langle |CHSH|\rangle\approx 2.25##