Question: Let (fn), (gn) be sequences of bounded functions on A that converge uniformly on A to f, g, respectively. Show that (fngn) converges uniformly on

Let (fn), (gn) be sequences of bounded functions on A that converge uniformly on A to f, g, respectively. Show that (fngn) converges uniformly on A to fg.

Step by Step Solution

★★★★★

3.44 Rating (186 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To conclude I can say that let M ... 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

Document Format (1 attachment)

829-C-F-M (418).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Let E be a nonempty subset of R and f be a real-valued function defined on E. Suppose that fn is a sequence of bounded functions on E which converges to f uniformly on E. Prove that uniformly on E as...

Let f1 and f2 be bounded functions on (a, b). Show that L(f1) + L(f2)

A sequence of functions fn is said to be uniformly bounded on a set E if and only if there is an M > 0 such that |fn (x)

Math 125 A: Homework 5 Due Thursday, November 9 1. For n = 1, 2, let fn : E R and suppose that fn f uniformly for some function f . Show that if each fn is bounded, then f is bounded. 2. Let {fn } be...

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Please help me do last 4 parts about 6.2.6 not make explicit mention of the onv suggests the need for an analogous characterization of uniformly sequences of functions. As with all statements about...

I am really desperate for someone to answer all 4 parts of this question (d, e, f, and g) (I have already posted this question twice and no one has answered all 4 parts sufficiently). This is due in...

Please give a valid and clear readable proof, thanks 10. Let I be an interval. Suppose that {fa} converges uniformly to f on I and {gm} converges uniformly to g on I. (a) Prove that {fn + 911}...

Suppose that fn f and gn g, as n , uniformly on some set E R. a) Prove that fn + gn f + g and fn f f, as n uniformly on E for all R. b) Prove that fngn fg pointwise on E. c) Prove that if...

10. Show that linear combinations of sequences that converge in measure on a set of finite measure also converge in measure. Please use following theories to prove (no need to use all of them, 1 or 2...

a. Fill in the missing numbers in the following income statement: Note: Do not round intermediate calculations and round your answers to the nearest whole number, e.g. 32. Sales Costs Depreciation...

Qasim Omer works as a consultant on currency management at Linda Asset Management headquartered in Canada. His role requires Qasim to provide consultation to portfolio and fund managers within Linda...

A stock is expected to pay $ 1 . 1 5 $ 1 . 1 5 per share every year indefinitely and the equity cost of capital for the company is 8 . 5 8 . 5 % . What price would an investor be expected to pay per...

What are the methods used to evaluate channel members? Why is this important?

Round each decimal to the given place value. 1. -42.895, nearest hundredth 2. 16.34925, nearest thousandth

Write each number in standard notation. 1. Saturn is a distance of about 887 million miles from the Sun. 2. The tail of a comet can be over 600 thousand miles long.

Write each decimal in words. 1. -23.45 2. 0.00345 3. 109.23 4. 200.000032

Find the Annual Recovery for Year 1 . Method = MACRS Purchased = Nov 0 5 Cost = 1 2 . 0 0 0 Recovery Class = 3 Annual Recovery for Year 1 =

Worthington Corporation has declared an annual dividend of $0.8 per share. For the year just ended, earnings were $8 per share. a. Worthington's payout ratio is ____________ percent. (Input answer as...

Given the following information, what is the variance of the returns on a portfolio that is invested 40 percent in both Stocks A and B, and 20 percent in Stock C? (probability of state occurring,...