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    Notes
    ----
    [1] Note that the proponents of protective measurement did not give an
explanation of the charge density. According to them, this type of measurement
implies that the wave function of a single quantum system is ontological, i.e.,
that it is a real physical wave (Aharonov, Anandan and Vaidman 1993).
    [2] The Hilbert space is a compete vector space with scalar product. The
state vector in a Hilbert space contains proper vectors normalizable to unity
as well as improper vectors normalizable only to the Dirac delta functions. The
exact nature of the Hilbert space depends on the system; for example, the state
space for position and momentum states is the space of square-integrable
functions.
    [3] For a
continuous property such as position, P(x) = || 2 is the
probability density at x, and P(x)dx is the probability of obtaining 
measurement result between x and x + dx.
    [4] By contrast, in a conventional impulse measurement the initial position
of the pointer is well localized around zero, and thus the conjugate momentum P
has a very large uncertainty which leads to a very large uncertainty in the
Hamiltonian of the measurement (2.1).
    [5] In order to read the position of pointer, an impulse position
measurement needs to be made after the weak measurement, and this will lead to
a