(i) If 1 and 1 are two measures on ((, A), then show that 1 2 is also a measure, where (A) 1 (A) 2 (A), A ( A (ii) if at least one of the measures 1 and 2 is complete, then so is ...

i We have to show that is nonnegative 0 and is additive Indeed A 1 A 2 A 0 1 2 0 i 1 A i 1 i 1 A i ...

(i) If 1 and 1 are two measures on ((, A), then show that = 1...

Question:

(i) If μ1 and μ1 are two measures on ((, A), then show that μ = μ1 + μ2 is also a measure, where μ (A) = μ1 (A) + μ2 (A), A ( A.
(ii) if at least one of the measures μ1 and μ2 is complete, then so is μ

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Measure Theoretic Probability

ISBN: 978-0128000427

2nd edition

Authors: George G. Roussas

See More Books

Question Posted: Mar 25, 2016 03:22 AM

See More Questions

Two measures of health care are the mean number of people per physician, and the percentage of the population who reside fewer than 5 km from a physician. In the table below, the 10 provinces are...
If a surveyor measures differences in elevation when making plans for a highway across a desert, corrections must be made for the curvature of the earth. (a) If R is the radius of the earth and L is...
If 1 and 2 are supplementary angles and if the measure of 2 is 17 times the measure of 1, determine the measures of the two angles.
The population of a certain colony of bacteria increases by 5% each hour. After 7 hours, what is the percent increase in the population over the initial population?
Where could an auditor look to find evidence of (a) Losses on purchase commitments or (b) Unrecorded liabilities to vendors?
Oregon Exchange Company completed the following long-term investment transactions during 2021: At year-end, the fair value of the Columbus stock is $30,100. The fair value of the Nashua stock is...
Explain the different types of static and dynamic stability.
1. Describe and evaluate what Pfizer is doing with its PfizerWorks. 2. Do you think this arrangement would work for other types of organizations? Why or why not? What types of organizations might it...
Explain each question with as much detail as possible. Explain why it is important for pay to be fair internally and what are the consequences if it is not. Demonstrate the importance of pay...
An engineer at a semiconductor company wants to model the relationship between the device HFE (y) and three parameters: Emitter-RS (x1), Base-RS (x2), and Emitter-to-Base RS (x3). The data are shown...
Consider the measure space ((, A, ), and suppose that A is complete with respect to . Let f, g : ( ( be such that (f ( g) = 0. Then show that, if one of f or g is measurable, then so is the other.
(i) Show that the class C3 consists of the unions of any two members of the class C2. (ii) Also, show that C3 is closed under complementation and the formation of the union of any two of its members....
It is necessary to fabricate an aligned and discontinuous glass fiber-epoxy matrix composite having a longitudinal tensile strength of 1200 MPa (175,000 psi) using a 0.35 volume fraction of fibers....
Why is it not always possible or feasible to select the best route for a shipment?
You just learned about promotion and distribution (product placement).Consider how this content relates to other areas of business. What information would you need to plan for how promotion impacts...
How can new technologies improve supply chain management?
To what extent do you believe a supply chain can be redesigned to compensate for poor product design or poor product quality?
If the leader of a company, such as Dan Cathy, CEO of Chick-fil-A, publicly takes a stand you do not agree with, discuss if this behavior changes your interest in the product.
Are there any measures of performance that can be calculated for the M/M/1 model but not the M/M/s model?
What are the risks and liability factors in an audit? What are the implications to the auditor? What are the implications to the organization? How can the auditor mitigate these risks and liability...
An experiment consists of tossing a die and then flipping a coin once if the number on the: die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4H, for...
Two jurors are selected from 4 alternates to serve at a murder trial. Using the notation A1 A3, for example, to denote the simple event that alternates 1 and 3 are selected, list the 0 elements of...
Four students are selected at random from a chemistry class and classified as male or female. List the elements of the sample space Si using the letter M for "male" and F for "female." Define a...
www The sugar cane industry is a big industry on Hawaii. Raw sugar cane is first cut from the fields, then chopped and shredded. The raw cane contains 15 wt% sucrose, 25 wt% solids, and water, along...
What does a manager who subscribes to Theory X believes ? Explain thoroughly.
Keri, in forming a new corporation, transfers land to the corporation in exchange for 100 percent of the stock of the corporation. Keri's basis in the land is $295,000, and the corporation assumes a...

(i) If 1 and 1 are two measures on ((, A), then show that = 1...

Question:

Step by Step Answer:

i We have to show that is nonnegative 0 and is additive Indeed A 1 A 2 A 0 1 2 0 i 1 A i 1 i 1 A i ...View the full answer

An Introduction to Measure Theoretic Probability

Students also viewed these Statistics questions