On a certain class of $g$-functions for subshifts
  A property $(D)$ of subshifts was defined in: Wolfgang Krieger, On $g$-functions for subshifts, IMS Lecture Notes- Monograph Series, Vol. 48, Dynamics & Stochastics (2006) 306 - 316, arXiv:math.DS/0608259. With a view towards a theory of $g$-fnctions beyond the case of finte type subshifts partially defined continuous $g$-functions of property $(D)$ subshifts are studied. 
Wolfgang Krieger