Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. let Ω be any set and let f be the collection of

Let Ω be any set and let F be the collection of all subsets of...

60.1K

Verified Solution

Question

Advance Math

Let Ω be any set and let F be the collection of all subsets of Ωthat are either countable or have a countable complement. (Recallthat a set is countable if it is either finite or can be placed inone-to-one correspondence with the natural numbers N = {1, 2, . ..}.)

(a) Show that F is a σ-algebra.

(b) Show that the set function given by

μ(E)= 0 if E is countable ;

μ(E) = ∞ otherwise


is a measure, where E ∈ F.

Answer & Explanation Solved by verified expert
3.6 Ratings (385 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Finance
1.2K views

Stevens Textile Corporation's 2018 financial statements are shown below: Balance Sheet as of December 31, 2018 (Thousands...

Operations Management
1.2K views

Project Management question: Prior to creating Status Report, what should I \"double check\"?

Biology
1.2K views

What is the difference between double helix, triple helix and quadriplex              structure in in nucleic acid molecules?...

Mechanical Engineering
1.2K views

Give me an introduction to the study of polymer of materials ?

Basic Math
1.2K views

Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records,...

Advance Math
1.2K views

Explain the difference between simple and compound interest and describe a scenario when the benefits of one...

Calculus
1.2K views

Find the length of the following two dimensional curve T r t 3 cos t...

Algebra
1.2K views

Review The graph of the linear function x is shown below If the function is...

Accounting
1.2K views

Lopez Company is considering replacing one of its old manufacturing machines. The old machine has...

Accounting
1.2K views

MC Qu. 13-67 Kingsbury Manufacturing has net sales revenue of. 3 Kingsbury Manufacturing has net...

Accounting
1.2K views

Enviro Company issues 8%, 10-year bonds with a par value of $290,000 and semiannual interest...

Accounting
1.2K views

Class Discussion Question: Variance analysis doesn't help us solve problems, it just tells us what...