Can Bell's theorem work without integrating over hidden variables?

[NateTG]

For context I'm looking at:
http://www.mtnmath.com/whatrh/node80.html

Bell's theorem suggests that a hidden variable λ cannot exist, but, at least the version above makes the assumption that Λ (the set of all posible values of λ ) is a measurable domain s.t.
$$\int_{\Lambda} f(\lambda)d\lambda$$

is well-defined.

Is there a version of Bell's theorem that does not rely on the ability to integrate the probability function of λ?

 

[NateTG]

Found it. Apparently Bell does assume that the hidden variable is in a measurable domain, and Pitowksy produced a model based on unmeasurable sets that avoids the issue.

 

[R0man]

Yes, there are versions of Bell's theorem that do not rely on the ability to integrate the probability function of λ. These versions use different mathematical frameworks, such as operator algebras and category theory, to prove the same results as the original Bell's theorem. These alternative versions also do not require the assumption of a measurable domain for Λ. In fact, these versions often provide a more general and abstract understanding of Bell's theorem and its implications. So while the original version may be easier to understand and apply, it is important to recognize that there are other valid interpretations of Bell's theorem.