True or false: if (f in mathcal{L}^{1}) we can change (f) on a set (N) of measure
Question:
True or false: if \(f \in \mathcal{L}^{1}\) we can change \(f\) on a set \(N\) of measure zero (e.g. by
\[\tilde{f}(x):= \begin{cases}f(x) & \text { if } x otin N \\ \beta & \text { if } x \in N\end{cases}\]
where \(\beta \in \overline{\mathbb{R}}\) is any number) and \(\tilde{f}\) is still integrable, even \(\int f d \mu=\int \tilde{f} d \mu\).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (1 review)
Data from theorem 112 i ii Data from corollaries 113 ...View the full answer
Answered By
Muhammad Umair
I have done job as Embedded System Engineer for just four months but after it i have decided to open my own lab and to work on projects that i can launch my own product in market. I work on different softwares like Proteus, Mikroc to program Embedded Systems. My basic work is on Embedded Systems. I have skills in Autocad, Proteus, C++, C programming and i love to share these skills to other to enhance my knowledge too.
3.50+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Business questions
-
The site http://virtualpiano.net features an online player piano. If you click on the Key Assist menu just above the piano keyboard, and then Keyboard Keys, you will see that each key is labelled...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
We discussed in the text that the market failure that emerges in the presence of externalities can equally well be viewed as a failure of markets to exist, and we discussed the related idea that...
-
A rectangular loop of wire with sides 0.20 and 0.35 m lies in a plane perpendicular to a constant magnetic field (see part a of the drawing). The magnetic field has a magnitude of 0.65 T and is...
-
For the component described in the problem indicated, determine (a) The principal mass moments of inertia at the origin, (b) The principal axes of inertia at the origin. Sketch the body and show the...
-
Wilson, Player and Sharp are in partnership. They shared profits in the ratio 2:4:3. It is decided to admit Titmus. It is agreed that goodwill is worth 72,000 and that it is to be brought into the...
-
Revenue Recognition} Mary Wade owns a small business that rents parking spaces to students at the local university. Mary's typical rental contract requires the student to pay the year's rent of \(\$...
-
If you invest $9,000 today, how much will you have? a. In 2 years at 9 percent? b. In 7 years at 12 percent? c. In 25 years at 14 percent? d. In 25 years at 14 percent (compounded semiannually)?
-
4. The population P (t) of certain bacteria culture in an environment over time t in minutes is modeled by the following ODE: P' + 2tP : e\"2 sin(3t) Suppose initially there are 5000 bacteria. (a)...
-
Every countable set is a \(\lambda^{1}\)-null set. Use the Cantor ternary set \(C\) (see Problem 7.12) to illustrate that the converse is not true. What happens if we change \(\lambda^{1}\) to...
-
Integrating complex functions. Let \((X, \mathscr{A}, \mu)\) be a measure space. For a complex number \(z=x+i y \in \mathbb{C}\) we write \(x=\operatorname{Re} z\) and \(y=\operatorname{Im} z\) for...
-
Q1) using the project life cycle develop a matrix showing when various sources of conflict occur. Q2) Describe the communications process in place on your project or in your organization. Q3) List...
-
Express the following first-order system as a single higher-order differential equation and solve using the given initial conditions. Make sure to change the initial conditions appropriately....
-
How can intercultural dialogue be leveraged to address global conflicts, and what role do cultural intermediaries play in fostering reconciliation and understanding among disparate cultural groups ?
-
Based on - The framers of the United States Constitution intentionally built points of conflict or tension into the constitutional system for several reasons: Separation of Powers : The framers...
-
Tom is a Health Care Assistant in a residential care facility. One afternoon, he observes that Mrs. White seems upset. He asks her if anything is wrong and she starts to cry. She tells Tom that her...
-
When considering an eportfolio tool usage to showcase your work and achievement. What does this provide to potential employers? Would a short blog or video be necessary to capture the attention of...
-
The market value of a corporation as a whole can be estimated by multiplying the number of shares of common stock times the market value at any given time. The corporations book value is simply the...
-
When the concentration of a strong acid is not substantially higher than 1.0 10-7 M, the ionization of water must be taken into account in the calculation of the solution's pH. (a) Derive an...
-
Distinguish between the micro and macro views of marketing. Then explain how they are interrelated, if they are.
-
Refer to Exhibit 1-1, and give an example of a purchase you made recently that i n volved separation of information and separation in time between you and the producer. Briefly e x plain how these...
-
Describe a recent purchase you made. Indicate why that particular product was available at a store and, in particular, at the store where you bought it.
-
Rapid Corp. makes two products: C and D . The following data have been summarized: View the Data and the Photo attached. The company plans to manufacture 2 5 0 units of each product. Calculate the...
-
The Murdock Corporation reported the following balance sheet data for 2 0 2 4 and 2 0 2 3 : Additional information for 2 0 2 4 : Sold available - for - sale debt securities costing $ 6 9 , 5 0 0 for...
-
ABC Inc. has 1 5 , 0 0 0 $ 2 . 5 0 cumulative preferred shares and 7 5 , 0 0 0 common shares outstanding. There were no dividends declared or paid in the last 2 years, but the Company declared $ 1 2...
Study smarter with the SolutionInn App