 The random variable is then a function from any outcome to a quantity, such that the outcomes leading to any useful subset of quantities for the random variable have a well-defined probability.When formula_15 is a topological space, then the most common choice for the σ-algebra formula_93 is the Borel σ-algebra formula_97, which is the σ-algebra generated by the collection of all open sets in formula_15.In such case the formula_82-valued random variable is called an formula_15-valued random variable.