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I'm asking from a mathematical aspect, please be as exact as possible.

Suppose A is an observable, and B a Borel set in R (real numbers). Without further assumptions on A, I would like a general expression for the probability of measuring one of the values from B for A.

The reason for my question is that it seems I'm stuck if A hasn't got any eigenvalues (like position X), and can't be associated with a wavefunction (like position X), or put in position representation.

Please notice that the two identical brackets have opposite interpretations.

*For example, for X, the answer would be the Lesbegues integral of [tex]\[

\left| \psi \right|^2

\]

[/tex] over B.

Suppose A is an observable, and B a Borel set in R (real numbers). Without further assumptions on A, I would like a general expression for the probability of measuring one of the values from B for A.

The reason for my question is that it seems I'm stuck if A hasn't got any eigenvalues (like position X), and can't be associated with a wavefunction (like position X), or put in position representation.

Please notice that the two identical brackets have opposite interpretations.

*For example, for X, the answer would be the Lesbegues integral of [tex]\[

\left| \psi \right|^2

\]

[/tex] over B.

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