Let ((X, mathscr{A}, mu)) be a finite measure space, (1 leqslant p
Question:
Let \((X, \mathscr{A}, \mu)\) be a finite measure space, \(1 \leqslant p<\infty\) and \(f \in \mathcal{L}^{p}\). Show that for \(m:=\int f d \mu\) and all \(a \in \mathbb{R}\) the following inequality holds:
\[2^{-p} \int|f(x)-m|^{p} \mu(d x) \leqslant \int|f(x)-a|^{p} \mu(d x)\]
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 75% (4 reviews)
Using Hlders inequality we get faP a 1f1aP 2P P aP Since X o this shows that both si...View the full answer
Answered By
MICHAEL KICHE
I was employed studypool for the first time in tutoring. I did well since most of my students and clients got the necessary information and knowledge requested for. I always submitted the answers in time and followed the correct formatting in answering eg MLA or APA format,
Again I worked with the writers bay where I did writing and got many clients whom we worked with so closely. They enjoyed every single service I delivered to them. My answers are always correct.
4.70+
13+ Reviews
53+ Question Solved
Related Book For
Question Posted:
Students also viewed these Business questions
-
1. What is an external recruitment source? Identify a recruitment source for a server at the Cheesecake Factory and why it would be effective. 2. What is an external recruitment method? Identify a...
-
Let \((X, \mathscr{A}, \mu)\) be a general measure space and let \(u \in \bigcap_{p \geqslant 1} \mathcal{L}^{p}(\mu)\). Then \[\lim _{p ightarrow \infty}\|u\|_{p}=\|u\|_{\infty}\] where...
-
Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...
-
In Exercises 116, evaluate each algebraic expression for the given value or values of the variable(s). x 2 - 4(x - y), for x = 8 and y = 3
-
Calculate the total binding energy, and the binding energy per nucleon, for (a) 6/3Li, (b) 208/82Pb. Use Appendix B.
-
Give an example not presented in the book that demonstrates how communication technology has advanced in the past five years. How has this technology affected the management process?
-
The compressive strength, in kilopascals, was measured for concrete blocks from five different batches of concrete, both three and six days after pouring. The data are as follows: Can you conclude...
-
The following are the Class Companys unit costs of manufacturing and marketing a high-style pen at an output level of 20,000 units per month: Manufacturing cost Direct materials ......$1.00 Direct...
-
The Sunshine Oil Company buys crude vegetable oil. Refining this oil results in four products at the splitoff point. A, B, C, and D. Product C is fully processed by the splitoff point. Products A, B,...
-
Prove the rules (14.2) for Cartesian products. Equation 14.2 (U4) x B=U(A B), (NA) x B=n(A B), (A x B) n (A' x B') = (ANA') x (BnB'), A x B= (X x B) \ (A x B), AXBCA' XB'ACA' und BCB', (14.2)
-
Use Jensen's inequality (Example 13.14 (i), (ii)) to derive Hlder's inequality and Minkowski's inequality. Use \[\Lambda(x)=x^{1 / q}, x \geqslant 0, \quad w=|f|^{p} \quad \text { and } \quad...
-
Imagine you are an innovation leader. Discuss how you will help your team create an innovation culture.
-
(A) We are given three diffent vectors: A = 6-3, B=-11+5j and C = A + B. (1) C = 2, (2) C = 51, (3) C = 5 + 2), (4) C=7+8 What is C in component form? A. 3 B. 1 C. 4 D. 2 Using the same three vectors...
-
Q7) Estimated investment function for Turkey between 1951-1976: where I: investment, Y: GNP, M: Imports. Following information is given = 1633.55 + 154.32Y+0.12Mt + 584.54D-41.42DtYt + 0.34DtMt i)...
-
Q4) We are trying to analyse the money spent for entertainment (ENT) in Turkey. Suppose we define: gender (G) as male or female; nationality (N) as Turkish or foreign; and marital status (M) as...
-
Consider the linear model: Y;= a + a (X - X) + U. Find the OLS estimators of ag and a. Compare with the OLS estimators of 30 and 31 in the standard model discussed in class (Y = 30 +3X; + ui).
-
1. A monopolist produces two commodities that are substitutes and having demand functions: X-8-P+P and X=9+P-5P, where 1,000 X, units of first commodity are demanded if its price is Rs P, per unit...
-
Matching debit and credit terminology with account titles Required Indicate whether each of the following accounts normally has a debit balance or a credit balance. a. Common Stock b. Prepaid Rent c....
-
Show that the peak of the black body spectrum as a function of ? is given by eq. (22.14) kg T Wmax = 2.82
-
List and describe the technologies used in this case study.
-
In what sense are U.S. farms now digital firms? Explain your answer.
-
How is information technology changing the way farmers run their business?
-
Indicate the referential integrity constraints (primary and foreign key relationships) using arrows. Clearly indicate datatype for each attribute. Test(FAA_no, name, score) Plane(reg_no, Model_no)...
-
Given the following C++ code snippet, what is the value of num3? Your answer must be exact. int num1, num2, num3; int *p_num1 - &num1; int *p_num2 &num2; *p_num1 15; *p_num2 10; * num3 = *p_num1...
-
:Obtain the transfer function Eo(s)/Ei(s) of the electrical circuit shown in Figure R ww R www
Study smarter with the SolutionInn App