Let f be measurable and B a Borel set. Then f-1[B] is a measurable set....

60.2K

Verified Solution

Question

Advance Math

Let f be measurable and B a Borel set. Then f-1[B] is a measurable set. [Hint: The class of sets for which f-1[E] is measurable is a ?-algebra.

Answer & Explanation Solved by verified expert

4.3 Ratings (861 Votes)

Proof Let E f1E is Lebesgue measurable Since inverse images are well behaved with respect to all the usual set operations and the family of Lebesgue measurable sets is a algebra it is easy to see that is a algebra Here are the details of that Suppose E Then f1E is Lebesgue measurable Consequently f1E f1E 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

Let f be measurable and B a Borel set. Then f-1[B] is a measurable set....

60.2K

Verified Solution

Question

Advance Math

Let f be measurable and B a Borel set. Then f-1[B] is a measurable set. [Hint: The class of sets for which f-1[E] is measurable is a ?-algebra.

Answer & Explanation Solved by verified expert

Get Answers to Unlimited Questions

Membership Benefits:

Other questions asked by students

Required:1. & 2. Prepare journalentries to record the transactions for April and post them...Required:1....

Which one of these salts will form a basic solution upon dissolving in water? A) KBr B) KClO3 C)...

What would happen if at rest, there was no concentration gradient for Na+ or K+? You have...

A uniform cylinder of radius 11 cm and mass 24 kg is mounted so as to...

5 Compare the speeds of waves of different amplitudes and frequencies in a given medium

7) To determine the cost of goods sold, to report on the income statement, multiply...

1: Using the trditional approach to assigning overhead costs to academic programs: Predetermined overhead rate:...

Joumalize the transactions. (Credit account titles are automatically indented when the amount is entered. Do...

The total of all employees' insurable earnings for the current remittance period is $54,200.00. What...

The Monarch Division of Allgood Corporation has a current ROI of 14 percent. The company...

The investor is long 100 shares PGS at $51 and writes one PGS May 55...

On April 17, 2024, the Loudstone Mining Company purchased the rights to a copper mine....