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Position--momentum uncertainty relation for the average confidence width
We introduce the average confidence width $Δ_{a} x=\int_0^1Δ_{c} x (θ)\,\mathrm{d}θ$: the confidence width $Δ_{c} x(θ)$---the measure of the smallest region of position space carrying probability $θ$---averaged over all confidence levels. It is the first moment of the decreasing rearrangement of the
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