I've been reading through Grimmett's and Stirzaker's Probability and Random Processes and on page 33 they state:
For the moment we are concerned only with discrete variables and continuous variables. There is another sort of random variable, called 'singular', for a discussion of which the reader should look elsewhere. A common example of this phenomenon is based upon the Cantor ternary set (see Grimmett and Welsh 1986, or Billingsley 1995.) Other variables are 'mixtures' of discrete, continuous, and singular variables.
I looked on Google Scholar for the two references mentioned in the excerpt, but haven't had any luck locating them.
Can someone explain what a singular random variable is and how it differs from the continuous and discrete variants?