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Watanabe, Sagawa, and Ueda defined the measurement error of an observable and
the disturbance to an observable by measurements for finite-dimensional systems
on the basis of quantum estimation theory and derived uncertainty relation
inequalities of error-error and error-disturbance types. This paper extend the
Watanabe-Sagawa-Ueda uncertainty relations to infinite-dimensional systems
employing the Fr\'echet derivative. We present a classical estimation theory
and a quantum estimation theory, both of which are formulated for parameter
spaces of infinite dimensions. An improvement in the derivation method makes
the resulting uncertainty relation inequalities tighter than original ones.
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