Stanford Encyclopedia of Philosophy
Supplement to The KochenSpecker Theorem
Derivation of STAT FUNC
The result is proved for a pure state and a nondegenerate discrete
observable A with eigenvalues a_{i}.
We first rewrite the statistical algorithm for projection
operators:
(1) 

For an arbitrary function f: R
R (where R is the set of real
numbers) we define the function of an observable A as:
Moreover, we introduce the characteristic function
_{} of a number a as:
As a result, we can rewrite a project operator
_{} as:
(2) 

and thus the statistical algorithm as:
We also use a simple mathematical property of characteristic
functions:
whence we can also write:
(3) 

Then:
Hence:
Now since
which is STAT FUNC.
Return to The KochenSpecker Theorem
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