  Lueders theorem states that two observables commute if measuring one of them
does not disturb the measurement outcomes of the other. We study measurements
which are described by continuous positive operator-valued measurements (or
POVMs) associated with coherent states on a Lie group. In general, operators
turn out to be invariant under the Lueders map if their P- and Q-symbols
coincide. For a spin corresponding to SU(2), the identity is shown to be the
only operator with this property. For a particle, a countable family of
linearly independent operators is identified which are invariant under the
Lueders map generated by the coherent states of the Heisenberg-Weyl group, H_3.
The Lueders map is also shown to implement the anti-normal ordering of creation
and annihilation operators of a particle.
