Given two functionals f and g on X, define (f g)(x) = max{f (x), g(x)} (f

Question:

Given two functionals f and g on X, define
(f ∨ g)(x) = max{f (x), g(x)}
(f ∧ g)(x) = min{f (x), g(x)}
If f and g are continuous, then so are f ∨ g and f ∧ g.

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

Step by Step Answer:

Related Book For book-img-for-question

Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

See More Books

Question Posted: May 02, 2016 11:39 AM

See More Questions

The dynamic programming problem (example 2.32) subject to xt+1 G(xt), t = 0, 1, 2, . . . , x0 X gives rise to an operator on the space B(X) of bounded functionals (exercise 2.16). Assuming that...
If f, g are continuous functionals on a metric space X, then f + g is continuous f is continuous for every R Therefore the set of all continuous functionals on X is a linear space.
If f, g are continuous functionals on a metric space X, then their product fg defined by (fg)(x) = f(x)g(x) is continuous.
TDS is a national delivery company based at Thornton Science Park. They employ 5 0 staff including administration, vehicle drivers, and warehouse workers. Their system is reliant on IT systems. Their...
According to Beverage Digest/Maxwell Report, the distribution of market share for the top seven soft drinks in the United States was: Coca-Cola 17.9%, Pepsi-Cola 11.5%, Diet Coke 9.7%, Mountain Dew...
What are the key phases of market planning?
17-5. El costo por contacto es elevado con el elemento de _________ la mezcla promocional .
Management is responsible for establishing effective internal control for its organization, including measures to prevent, deter, and detect fraud. Appendix 7A on pages 294296 describes antifraud...
Please answer problem #10 part B, SHOWING ALL WORK ACCORDINGLY. Thank you! The following information pertains to Sunland Company 1. Cash balance per books, August 31, $ 7,374 2. 3. Cash balance per...
The chief economic adviser of a small open economy makes the following announcement: "We have good news and bad news. The good news is that we have just had a temporary beneficial productivity shock...
Show that the sequence of polynomials converges uniformly on any compact subset S . x2 2! 3! + k=0
Use proposition 2.3 to provide an alternative proof of theorem 2.2 Theorem 2.2 A continuous functional on a compact set achieves a maximum and a minimum. Proof Let M = supxX f (x). There exists a...
What volume of n-hexane is required to decrease the concentration of X in Problem 31-11 to 1.00 x 10-4 M if 25.0 mL of 0.0500 M X is extracted with (a) 25.0-mL portions? (b) 10.0-mL portions? (c)...
Steve Reese is a well-known interior designer in Fort Worth, Texas. He wants to start his own business and convinces Rob ODonnell, a local merchant, to contribute the capital to form a partnership....
One of the main purposes of evaluation research is: a. reexamining previously collected data. b. monitoring and improving programs. c. generating rich descriptions of individual perspectives. d....
10.13 Sweetlip Ltd and Warehou Ltd are two family-owned flax-producing companies in New Zealand. Sweetlip Ltd is owned by the Wood family and the Bradbury family owns Warehou Ltd. The Wood family has...
distribution that is skewed to the right instead of being normally distributed. Assume that we collect a random sample of annual incomes of 50 statistics students. Can the distribution of incomes in...
Swain Athletic Gear (SAG) operates six retail outlets in a large Midwest city. One is in the center of the city on Cornwall Street and the others are scattered around the perimeter of the city....
The No-Ash Coal Company recorded the following transactions. Indicate how each would be treated on a statement of changes in financial position, assuming that funds are defined as the cash balance....
D Which of the following is considered part of the Controlling activity of managerial accounting? O Choosing to purchase raw materials from one supplier versus another O Choosing the allocation base...
In Exercise 6-44, data was presented on the cold start ignition time of a particular gasoline used in a test vehicle. A second formulation of the gasoline was tested in the same vehicle, with the...
The College of Engineering and Applied Science at Arizona State University had a VAX computer system. Response times for 20 consecutive jobs were recorded and are as follows: (read across) Construct...
The following data are the viscosity measurements for a chemical product observed hourly (read down, then left to right). (a) Construct and interpret either a digidot plot or a separate stem-and-leaf...
Draw an interaction diagram for the following contract: If a collaboration diagram is used, be sure that all messages' sequence numbers are shown. Contract: Scheduling a Flight Operation:...
Columbus Industries makes a product that sells for $37 a unit. The product has a $29 per unit variable cost and total fixed costs of $10,000. At budgeted sales of 1,950 units, the margin of safety...
18. Suppose that Maxima shares are selling for $10 per share and you own a call option to buy Maxima shares at $7.50. The intrinsic value of your option is:

Given two functionals f and g on X, define (f g)(x) = max{f (x), g(x)} (f

Question:

Step by Step Answer:

For any the upper and lower contour sets ...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions