Therefore, if the system is prepared in a state ψ ψ , then the probability of the measured position of the particle belonging to a Borel set B is ‖ ‖ μ μ X ( B ) ( ψ ψ ) ‖ ‖ 2 = ‖ ‖ χ χ B ψ ψ ‖ ‖ 2 = ∫ ∫ B | ψ ψ | 2 μ μ = π π X ( ψ ψ ) ( B ) , where μ μ is the Lebesgue measure on the real line.