  We study universally valid uncertainty relations in general quantum systems
described by general $\sigma$-finite von Neumann algebras to foster developing
quantitative analysis in quantum systems with infinite degrees of freedom such
as quantum fields. We obtain the most stringent measurement-disturbance
relation ever, applicable to systems with infinite degrees of freedom, by
refining the proofs given by Branciard and one of the authors (MO) for systems
with finite degrees of freedom. In our proof the theory of the standard form of
von Neumann algebras plays a crucial role, incorporating with measurement
theory for local quantum systems recently developed by the authors.
