The set of properties that must hold, for the sequence of actions in the Use Case scenario to operate correctly.

This is not the same as the set of exceptions that may be handled by the scenario.
Example: The scenario assumes that subsystems A, B and C will have already been initialized.

Assumptions should be stated as True or False declarative statements. A robust Use Case has a very small number of assumptions.
NB: The Initial State is actually a part of the assumptions.