Problem 2 Let f be an absolutely continous function on (0, 1], and f E LP on 0,. Show that, for s...

Question

Question

Problem 2 Let f be an absolutely continous function on (0, 1], and f E LP on 0,. Show that, for sotne a >D and C>0, we have f

Please write clearly

Answer 1

Answer #1

* Given Tom-Re data is low as eP S-

Answer 2

Similar Homework Help Questions

(Limit of functions) Let f : 2-» C be a function, and assume that D(a, r)...

(Limit of functions) Let f : 2-» C be a function, and assume that D(a, r) C Q. We say that lim f(z) L Ď(a, 6) we have |f(z) Ll < e. if for any e > 0 there exists 6 > 0, such that for any z e (a) State the negation of the assertion "lim^-,a f(z) = L". (b) Show that lim- f(z) L if and only if for any sequence zn -» a, with zn a for...
Answer C 6. Let f be a continuous function on [0, oo) such that 0 f(z)...

Answer C 6. Let f be a continuous function on [0, oo) such that 0 f(z) Cl- for some C,e> 0, and let a = fo° f(x) da. (The estimate on f implies the convergence of this integral.) Let fk(x) = kf(ka) a. Show that lim00 fk(x) = 0 for all r > 0 and that the convergence is uniform on [8, oo) for any 6> 0. b. Show that limk00 So ()dz = a. c. Show that lim00 So...
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Sho...

Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Show that f E C(R) and that 1 cos(nx) f'(x)= 2-1 c) Show that 「 f#072821) f(x)dx = k=0 Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f...

Let Ich be a not cmety interval and We will say that is a Darboux function ie for any ab,a,beI and any between la) a...

Let Ich be a not cmety interval and We will say that is a Darboux function ie for any ab,a,beI and any between la) and e(b) there is a ce [ab such that P(C)=2. IF F is a Darboux Punction ls it a continous function? a couaterexample. Show or give Let Ich be a not cmety interval and We will say that is a Darboux function ie for any ab,a,beI and any between la) and e(b) there is a ce...
Let f(x) be a continous function defined on R. Consider the following function, g(x) = max{f(t)\t...

Let f(x) be a continous function defined on R. Consider the following function, g(x) = max{f(t)\t € [2 – 1, 2+1]}. Prove that g(x) is also continous. Hint: To prove g(x) is continous at x = xo. You can consider the continuity of f(x) at the two boundary point xo - 1 and xo +1. When x get close to xo, the points in (7 - 1, + 1) is close to xo - 1, xo + 1, or inside...
Problem 4: Let f: [0, 1] → R be an integrable function that is continuous at...

Problem 4: Let f: [0, 1] → R be an integrable function that is continuous at 0. Prove that lim f(") dx = f(0). n+Jo [ Hint: there are several approaches. It might help to first show that for a fixed 0 <b< 1, we have limn700 Sº f(x) dx = b. f(0). ]

Let X1....Xn be i.i.d sample with a continous distribution function F(.) and X(1)<......<X(n) are the orser-statistics...

Let X1....Xn be i.i.d sample with a continous distribution function F(.) and X(1)<......<X(n) are the orser-statistics of the sample. Let the constant Mp be defined by F(Mp)=p. Show that for 1≤k1≤k2≤ n, P{X(k1) ≤Mp ≤X(k2)}=P{k1 ≤Bionmial(n,p) k2}
Problem 4 (4 points each). Let S = R {0}. (a) Let f: S R be...

Problem 4 (4 points each). Let S = R {0}. (a) Let f: S R be f(x) = cos(1/x). Show that lim-0 f(x) does not exist. (b) For any fixed a > 0, let f: S+R be f(x) = rºcos(1/x). Show that lim -- f(x) = 0. (c) Find a value be R for which the function f: R+R given by f(x) = { 2" cos(1/x) if r +0, if x = 0, is continuous at 0. Is this b...
8. Let f (x) e, 0 > 0; x> 0 (1 1 +e (a) Show that...

8. Let f (x) e, 0 > 0; x> 0 (1 1 +e (a) Show that f(x) is a probability density function (b) Find P(X> x) (c) Find the failure rate function of X

number 3 please Hw4.1708.pd 1 2 TL (2) LP convergence vs. convergence in probability Let Xn,...

number 3 please Hw4.1708.pd 1 2 TL (2) LP convergence vs. convergence in probability Let Xn, nNbe a sequence of random variables and let X be another random variable. Given l < p < oo, we say that Xn converges to X in Lp if E(Xn-X") → 0 as n → x Show that this implies that Xn converges to X in probability (3) Monte Carlo Let f : 10, 1] → R be continuous and let Xn, n on...