An elementary outcome is one member of the sample space. For the ordered two-toss model, is one outcome; it contains both toss results. By contrast, “at least one head” is an event containing three outcomes. The outcome and the singleton set are different objects: when that singleton is measurable, the notation gives its probability. In the finite model below, every subset is measurable.
The word elementary refers to the chosen level of detail. An outcome can be an ordered pair, a sequence, or an entire realization of a point process. A random variable then extracts a numerical feature of that outcome; the window count of a point process is one example.
New to topics? Read the docs here!