Editing Information content (section)

==== Special case: constant random variable ====
If <math>b = a</math> above, <math>X</math> [[Degeneracy (mathematics)|degenerates]] to a [[constant random variable]] with probability distribution deterministically given by <math>X = b</math> and probability measure the [[Dirac measure]] <math display="inline">p_X(k) = \delta_{b}(k)</math>.  The only value <math>X</math> can take is [[Deterministic system|deterministically]] <math>b</math>, so the information content of any measurement of <math>X</math> is<math display="block">\operatorname{I}_X(b) = - \log_2{1} = 0.</math>In general, there is no information gained from measuring a known value.<ref name=":0" />