Random sets and does the Ellsberg paradox matter

Random sets might be considered from several possible viewpoints. A "Business-managerial" 'viewpoint' would prop the following definition : take all sets, list them and then pick one set from this list at random. An "Image analysis" 'viewp oint' would yield alternatively the following definition: take a grid of pixels; if some of these pixels are randomly colored in black or white, then the resulting picture is arandom set. Finally a "statistical" 'viewp oint' would yield the following definition:a random set is a confidence region for an estimated parameter. In the decision-making framework, a lottery defined on opportunities, a kind ofso-to say two-step lottery, might be viewed as a random set. Let us now turn to a mathematical definition. A random set is a measurable map from a given probability space to the p ower set equipp ed with some σ -algebra...