How the concept of information as average number of "yes"-"no" questions (bits) can be extended to intervals, p-boxes, and more general uncertainty

We explain how the concept of information as average number of "yes"-"no" questions (bits) can be extended to intervals, p-boxes, and more general uncertainty. For each type of information that we are soliciting, there are several ways to acquire this information. For example, if we are interested in measuring the value of a physical quantity x, we may use different types of sensors. No matter how accurate the sensor, the measured value x is, in general, different from the actual value x of the measured quantity.