What is a Nyquist's information in discrete measurements? We perform a measurement of some physical object, giving a result value in interval [0,1] in some units. The value has a gaussian statistical error of some known [itex]\sigma[/itex] (by order of magnitude comparable to 1). We do lots ([itex]\rightarrow \infty[/itex]) of such measurements of various real objects, our only a priori knowledge is that true values have some unknown distribution bounded within [0,1]. What is a maximal average information (in Shannon-Nyquist meaning) carried by such measurement? Intuition tells me that Nyquist's law should apply here (with some proportionality factor maybe). Had anyone read (or even better: written...) any article on such topics? I would be really grateful for a reference!