Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I wonder what benefits or purposes can be obtained, through studying measures completely in terms of some or all measurable mappings that can induce the measures on their codomains?

Since different measurable mappings defined from the same measure space to the same codomain can induce the same measures on their codomains, representing measures by measurable mappings actually induce more complication to consider.

For example,

  • In many probability examples/exercises, the questions being asked are entirely about the probability measures, but they are phrased completely in terms of random variables that induce the probability measures on their codomains.
  • Coupling, as I understand and if I understand correctly, study the relation between two probability measures, in terms of any pair of two random variables that have the two probability measures as their induced ones respectively.


share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.