  The Broad Histogram is a method designed to calculate the energy degeneracy
g(E) from microcanonical averages of certain macroscopic quantities Nup and
Ndn. These particular quantities are defined within the method, and their
averages must be measured at constant energy values, i.e. within the
microcanonical ensemble. Monte Carlo simulational methods are used in order to
perform these measurements. Here, the mathematical relation allowing one to
determine g(E) from these averages is shown to be exact for any statistical
model, i.e. any energy spectrum, under completely general conditions.
  We also comment about some troubles concerning the measurement of the quoted
microcanonical averages, when one uses a particular approach, namely the energy
random walk dynamics. These troubles appear when movements corresponding to
different energy jumps are performed using the same probability, and also when
the correlations between successive averaging states are not adequately
treated: they have nothing to do with the method itself.
