Let E be a set and  E   a σ -algebra of subsets of  E . Assume that the
 σ -algebra  E is  countably generated, i.e. generated by a countable collection
of subsets of E . 

          The measurable space  (E,E) is called the  state space and the
points of E are called  states. 

          The symbol  E will also be used to denote the
collection of extended real valued measurable functions on  (E,E) . 

          The symbols x,y,… denote states,  A, B, …   denote elements of the σ -algebra  E ,
and f,g,…   denote extended real valued measurable functions on  (E, E) .

Kernels