In summary we have to grow quite complicate if we want to understand what real randomness is.  Once clarified what it is, we can have the problem to assess what can be a random arrangement for an arbitrary set of objects, say \(\Omega\). Taking example of the algorithms used to get a given random sequence of  numbers from a give distribution, we can observe that probability itself can be used to infer the random sequence of a set from a random sequence in [0,1] by inverting the probability \(P\).
Random sampling is significant when the set of the domain is subdivided into disjoint parts: a partition. Therefore
Definition: Given a set (having the structure of a \(\sigma\)-algebra) \(\Omega\) let a partition of  \(\Omega\), denoted as: