sentences:  For a random measure formula_5, the integrals
  and
  formula_52
  
  for positive formula_2-measurable formula_41 are measurable, so they are random variables.The distribution of a random measure is uniquely determined by the distributions of
  
  for all continuous functions with compact support formula_41 on formula_1.For a fixed semiring formula_58 that generates formula_2 in the sense that formula_60, the distribution of a random measure is also uniquely determined by the integral over all positive simple formula_61-measurable functions formula_41.