The historical process is constructed to be a superprocess
which is enriched so as to contain information on genealogy. This
process together with a representation for the associated Palm
measures are used to describe the modulus of continuity and
equilibrium structure for a class of superprocesses, and to
establish that the super-Brownian motion in dimensions d^3 has
constant density with respect to the appropriate Hausdorff
Received by editor February 12,1990.
KEY WORDS AND PHRASES: Superprocess, historical process, Palm
measure, Hausdorff measure, modulus of continuity, equilibrium
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