Question: Let (X, A, ) be a measure space and let (fn)neN, and f, g be extended real-valued A-measurable and integrable functions on DE A.

Let (X, A, ) be a measure space and let (fn)neN, and

Let (X, A, ) be a measure space and let (fn)neN, and f, g be extended real-valued A-measurable and integrable functions on DE A. Suppose that 1. limn- fn = fa.e. on D. 2. limno fp fndu = fpfdu. 3. either fng on D for all n N or fn g on D for all n E N. Show that, for every EEA and ECD, we have limm / Sadje - fdp. = S n-x E E

Step by Step Solution

★★★★★

3.50 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The detailed ... 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 Mathematics Questions!

PROBLEM P5 (Sheet P5). M&A, an investment company, can invest in four stocks. From past data, the means/standard deviations of stocks and correlations are given in range C4:F5. The company likes...

Let (X, M, p) be a measure space and let f be a nonnegative measurable function. If A E M and 4(A) = 0 them show that SA fdu = 0.

Let (X, A, p) be a measure space and let f be an extended real-valued A- measurable function on X such that fx fdu

Please watch the video link and answer the following questions. https://youtu.be/VtvjbmoDx-I On January 22,1984, Apple produced one of the most famous Super Bowl ads of all time. Directed by Ridley...

Carpenter Inc. had a balance of $98,000in its quality-assurancewarranty liability account as of December 31, 2023. In 2024,Carpenter's warranty expenditures paid were $463,000. Its warrantyexpense 2...

Prepare Kyler Medias statement of cash flowsindirect methodfor the year ended December 31, 2022. KYLER MEDIA CORPORATION Income Statement Year Ended December 31, 2022 Service revenue 80,000...

Preview File Edit View Go Tools Window HIGHLIGHTS & NOTES Help 8. Case 4 - Coach Takes on China (2013).pdf (page 1 of 8) Coach Takes on China: Leveraging Distribution to Solve Unique Challenges Case...

4. ______________ shapes the culture for process improvement. a. stability b. standardize c. jidoka d involvment

E 1. Assume that all common stock is issued for cash. What amount of cash dividends is paid during 2021? 2. Assume that no additional notes payable are issued in 2021. What cash amount is paid to...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Terra Corporation (a C corporation) had an operating loss of $6,000 for 2021. Terra sold a number of investments in 2021 which resulted in a net long-term capital loss (NTLCL) of $9,000. In addition,...

Identify what is being oxidized and reduced in this redox reaction by assigning oxidation numbers to the atoms. 2Rb + MgCl2 ( 2RbCl + Mg

1 5 of 1 5 You can call law enforcement at any time you feel you require their assistance. True or False ( Please select an appropriate answer ) ATrueBFalse

A clock has an hour hand of length 4cm, a minute hand of length 5.5 cm and a second hand of length 6 cm. How quickly is the area of the quadrilateral formed by the centre of the clock and the tips of...

20mL of an 85m M solution of m -cresol, a monoprotic acid (pK a = 10.1) is neutralised by the addition of 15mL of a 140m M solution of potassium hydroxide. When using phenolphthalein as an indicator...

1. Under these circumstances, would Justin be wise to pursue a top-down or a bottom-up budgeting approach? Why? 2. What factors are most relevant in terms of creating a budget in this situation?...

Take BHP as manufacturing company in Australia.What kind of investment entry mode is the most suitable for BHP Company?Compare these different investment entry modes (joint venture, greenfield...

Sebelum pensiun, Pak Deden sering dikunjungi saudara-saudaranya, baik saudara yang dekat maupun saudara yang sudah jauh. Kalau pulang, mereka sering diberi oleh-oleh dan uang yang tidak sedikit....

Prove that limn (- l)k/k exists and is finite.

a) Let E be a nonempty subset of X. Prove that a is a cluster point of E if and only if for each r > 0, E Br(a) \ (a) is nonempty. b) Prove that every bounded infinite subset of R has at least one...

Let E1 be the unit interval [0, 1] with its middle third (1/3, 2/3) removed (i.e., E1 = [0, l/3]U[2/3, 1]). Let E2 be E1 with its middle thirds removed; that is, E2 = [0, 1/9] U [2/9, 1/31 U [2/3,...

A manufacturer conducted a pricing experiment to explore the effects of price decreases on sales of one of its breakfast cereals. The two largest supermarket chains in a particular area participated...

A crime victimization study was undertaken in a medium-size southern city. The main purpose was to determine the effects of being a crime victim on confidence in law enforcement authority and in the...

The data listed in the table on the following page are from an unpublished study by Harbin and others (1985). Subjects were young (ages 18 through 29) or old (ages 60 through 86) men. Each subject...