sentences:  (The most common example of a separable complete metric space is formula_4)
  A random measure formula_5 is a (a.s.) locally finite transition kernel from a (abstract) probability space formula_6 to formula_7.Being a transition kernel means that
  
  Being locally finite means that the measures
  satisfy formula_16 for all bounded measurable sets formula_17
  and for all formula_12 except some formula_19-null set
  Define
  
  and the subset of locally finite measures by
  
  For all bounded measurable formula_22, define the mappings
  
  from formula_24 to formula_25.Let formula_26 be the formula_3-algebra induced by the mappings formula_28 on formula_24 and formula_30 the formula_3-algebra induced by the mappings formula_28 on formula_33.