Show that the following functions defined on R are all Borel measurable, and hence Lebesgue measurable...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Show that the following functions defined on R are all Borel measurable, and hence Lebesgue measurable also on R: (a) f(x) = Jo if x is rational if r is irrational. (c) h(x) = sin a COS X (b) g(x) = I -I if x is rational if r is irrational. if x is rational if x is irrational. Show that the following functions defined on R are all Borel measurable, and hence Lebesgue measurable also on R: (a) f(x) = Jo if x is rational if r is irrational. (c) h(x) = sin a COS X (b) g(x) = I -I if x is rational if r is irrational. if x is rational if x is irrational.
Expert Answer:
Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Posted Date:
Students also viewed these mathematics questions
-
Show that the following functions belong to R*[0, 1] by finding a function Fk that is continuous on [0, 1] and such that Fk(x) = fk(x) for x [0, 1]\Ek, for some finite set Ek. (a) f1(x) := (x + 1)/x...
-
Show that the following equations have at least one solution in the given intervals. a. x cos x 2x2 + 3x 1 = 0, [0.2, 0.3] and [1.2, 1.3] b. (x 2)2 ln x = 0, [1, 2] and [e, 4] c. 2x cos (2x) (x ...
-
Show that the following functions (properly defined when necessary) are in L[0, 1]. (a) x ln x/1 + x2, (b) sin x/ln x, (c) (ln x)(ln(1 - x)), (d) In x/1 - x2.
-
Prepare a statement of profit or loss and other comprehensive income( year ending 31 march 2023) , and a statement of financial position as at 31 march 2023 for the Batliss Plc Bayliss Plc is a...
-
Using the data below, find i) The return on equity ii) The value of the firm using the M&M Propositions. Equity Value ........................................................$5,000,000 Debt Value...
-
In Problems 11 54, simplify each expression. Assume that all variables are positive when they appear. 8x3 350x
-
Could a contract be difficult to categorize as either public or private international law? What would such a contract look like?
-
Reggi Vineyards produces a full line of varietal wines. The company, whose fiscal year begins on November 1, has just completed a record-breaking year. Its inventory account balances on October 31 of...
-
Explain why clients may want to have a review, versus an audit. In detail, explain the differences between a certified audit and a review. In addition, what role does an internal auditor play in...
-
The evening manager of a restaurant was very concerned about the length of time some customers were waiting in line to be seated. She also had some concern about the seating times that is, the length...
-
Refer the following table. Focus Metals Inc. Comparative Balance Sheet Information: November 30 (millions of $) 2020 Cash 16 86 Accounts receivable (net). 386 232 60 53 Inventory Plant and equipment...
-
An extract of balances at 31 December 2022 showed accounts receivable control $60 610, allowance for doubtful debts $750, GST payable $1000 and bad debts expense $2500. Using the combined method,...
-
On 30 June 2023 R Williams decides to increase the allowance for doubtful debts from $1200 (created in 2022) to 5% of the accounts receivable control account balance of $49 995. Bad debts expense of...
-
a Prepare general journals for the following balance day adjustments at 30 June 2022: insurance prepaid $750 wages accrued $600 interest receivable $350 rent received in advance $495 ($450 + $45...
-
On 1 July 2021 L Bathurst had entered a 24-month contract with her tenant for rent of premises for $23 100 ($21 000 + $2100 GST) per annum to be paid monthly in advance. At the end of the financial...
-
Rent of $660 ($600 + $60 GST) was received in June for the month of July. The balance of the rent received account at 30 June before the adjustment was $7800. You are required to prepare the journals...
-
How did we get the contribution margin ratio and profit margin ratio? Also I wanted to ask that why are fixed costs divided by useful life in an income statement? Contribution Margin Ratio (%) Profit...
-
(8%) Problem 6: A student attaches a f= 3.5 kHz oscillator to one end of a metal rail of length L = 25 m. The student turns on the oscillator and uses a piezoelectric gauge at the other end to...
-
Let h(x) := e-1/x2 for x 0 and h(0) := 0. Show that h(n)(0) = 0 for all n N. Conclude that the remainder term in Taylor's Theorem for x0 = 0 does not converge to zero as n for x 0. [By L'Hospital's...
-
Let S2 : {x R : x > 0}. Does S2 have lower bounds? Does S2 have upper bounds? Does inf S2 exist? Does sup S2 exist? Prove your statements.
-
If I1 I2 In is a nested sequence of intervals and if In = [an; bn], show that a1 < a2 < < an < and b1 > b2 > bn > .
-
In the second quarter of 2021, personal consumption expenditures, exports, and imports increased. Investment and government expenditure decreased. Real GDP increased by 6.5 percent following a 6.3...
-
When real GDP increased in the second quarter of 2021, consumption expenditure, exports, and imports increased. Fixed investment decreased, which included a decrease in business inventory investment....
-
Explain why higher stock prices and higher real estate values are equivalent to saving. U.S. household wealth grew to \($136.9\) trillion in the first quarter of 2021. Rising stock prices added...
Study smarter with the SolutionInn App