Kernels

           Let $E$ be a set and  $\mathscr{E}$   a $\sigma$ -algebra of subsets of  $E$ . Assume that the
  $\sigma$ -algebra  $\mathscr{E}$ is  countably generated, i.e. generated by a countable collection
of subsets of $E$ . 

          The measurable space  $(E, \mathscr{E})$ is called the  state space and the
points of $E$ are called  states. 

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

          The symbols $x, y,\ldots$ denote states,  $A,? B,?\ldots$   denote elements of the $\sigma$ -algebra  $\mathscr{E}$ ,
and $f,g,\ldots$   denote extended real valued measurable functions on  $(E,? \mathscr{E})$ .

Kernels

原文：http://www.cnblogs.com/levin2013/p/3520011.html