Explore BrainMass

# Probabilities and Set Theory

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Please see the attached file for the fully formatted problems.

Let (Omega, A) be a measurable space, and P:A--> [0,infinity] an application such that P(AUB) = P(A) + P(B) when A,B E A and A intersection B = ø, and P(Omega) = 1 . Prove that the following statements are equivalent:
(i) P is a probability
(ii) P is continuous on the decreasing series:

(iii) P is continuous on the increasing series:

(iv) and ø

https://brainmass.com/math/discrete-math/probabilities-set-theory-13314

#### Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Let be a mesurable space, and an application such that when and ø, and . Prove that the following statements are equivalent:
(i) P is a probability
(ii) P is ...

#### Solution Summary

Proofs are provided for proabilities expressed with set theory. The solution is detailed and well presented.

\$2.49