Question: Let X be an arbitrary set. A be a class of subsets of X and I be an extended real-valued function : A(0, +00).

Let X be an arbitrary set. A be a class of subsets of X and I be an extended real-valued function : A(0, +00). When is said to be countably sub-additive. (1) (ii) said to be a measure on A. (b) (i) Let (X.A.) be a measure space. Prove that, if (A) is an arbitrary sequence of sets in A, then (UA) (A)

Step by Step Solution

★★★★★

3.41 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To prove that is countably subadditive we need to show that for any countable sequence of sets Ak in ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Banking Questions!

How do social norms contribute to the maintenance of social order and stability, while also serving as mechanisms for social control and the enforcement of conformity?

Provided are the consolidated trial balances of a parent and its less-than-wholly-owned subsidiary. Account Dr (Cr) $5,000 105,000 10,000 80,000 (162,405) (10,000) (15,000) Current assets Property,...

Finance House ( FH ) sold an equipment, costing Rs . 6 0 , 0 0 0 , to a customer on installment sale basis on January 1 , 2 0 1 8 . Each installment of Rs . 4 0 , 0 0 0 will be received on every...

A data analyst decided to do all design work from home and wants to create a home office. The analyst needs a new computer for $1,900 and printer/scanner for $250. A vendor offers a financing option...

A rope of mass density lies in a heap on the floor. You grab an end and pull horizontally with constant force F. What is the position of the end of the rope, as a function of time, while it is...

Interview the manager of a local service business, such as a restaurant or hair salon. Identify the major decisions involved in planning that businesss service operations.

7. Follow all classroom and school procedures, like: bathroom; pencil; lunch and recess; morning; dismissal; and . . .

What proportion of secretaries of Fortune 500 companies has a personal computer at his or her workstation? You want to answer this question by conducting a random survey. How large a sample should...

A business has a market share of 20% and it competes in a market where the total market demand is 300,000 units. The price per unit and variable cost per unit are $25 and $10, respectively. If the...

Identify some differences between business organizations and government/not-for-profit organizations.

Consider the following situations: (Click the icon to view the situations.) Requirement 1. For each situation, identify the inventory method that you would use; or, given the use of a particular...

Addressing A large organisation has a CIDR block (192.168.128.0/18) and would like to give one subnet to each department as shown below. Develop a variable-length addressing scheme that best fits the...

Context: You are a Sales Account Manager and you manage a book of business made up of 100 restaurants (brands). Your main priority is Client Retention and Growth. You want restaurant businesses to...

Question1 diversity in the workplace. Please research 6 benefits of having a diverse workforce. Explain in detail how each of the benefits enable an organization to become more competitive and...

Your company intends to invest in FinTrans, a fintech company that facilitates convenient transfer of funds across borders. You will be able to influence FinTrans' product development so that your...

Sandy's Soda Co. is planning to purchase new equipment that costs $56,000 and will save on operating costs for the next 5 years as follows: $21,500 in year $23,100 in year 2; $19,000 in year 3;...

You are standing on the top of a building and throw a ball vertically upward. After 2 seconds, the ball passes you on the way down, and 2 seconds after that, it hits the ground below. a. What is the...

In the extension of an infinite field K by K(x,y), the intermediate field K(x) is Galois over K, but not stable (relative to K(x,y) and K). [See Exercise 9] Data from exercise 9 (a) If K is an...

Let be a concrete category and T: S the forgetful functor. If T has a left adjoint F : S , then F is called a free-object functor and F(X) (X S) is called a free F-object on X. (a) The category...

Proof that If K is finite and F is an algebraic closure of K, then Aut K F is abelian. Every element of Aut K F (except 1 F ) has infinite order.

A profit-sharing bonus was divided among four employeesMs. L, Mr. M, Ms. N, and Mr. Pin the ratio of 1.5:1: 0.75: 0.5, respectively. If Ms. N received $2000, how much did each of the others receive?

How should common area costs totalling $28,575 be allocated among commercial tenants A, B, C, and D if the costs are prorated based on leased areas of 1260, 3800, 1550, and 2930 square feet,...

Express each of the following ratios in its lowest terms. a. 0.18: 0.60: 0.45