Question: Let D be a dense set in R. Let f be an extended real-valued function on R such that {r: f(x) > a} is

Let D be a dense set in R. Let f be an

Let D be a dense set in R. Let f be an extended real-valued function on R such that {r: f(x) > a} is measurable for each a D. Show that f is measurable.

Step by Step Solution

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!

Determine the normal stress and shear stress acting on the inclined plane AB. Sketch the result on the sectioned element. 500 kPa 30 A F9-1

Let D be a nonsingular n Ã n diagonal matrix and let (a) Show that (b) Show that and dmin-min ldil dmax=max ld,il Isisn condi( D) = condoo (D) =-max dmax dmin cond2(D) =

Let d be a gauge on I: = (a, b) and suppose that I does not have a d-fine partition. (a) Let c : = (a + b). Show that at least one of the intervals [a, c] and [c, b] does not have a -fine partition....

Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model y = (0 + (0d + (1z + (1d (z + u; this is a general version of a model with an interaction between a dummy...

we regard the equation 3 as standard form of an UDE OI course the ODE has order k Note that the function X tX t is a vector valued function of the real variable t and as such it is a curve in R Each...

course the ODE has order k Note that the function X t X t is a vector valued function of the real variable t and as such it is a curve in R Each X has n components X t X 1 X 1 X t and therefore all...

(Revised 2024-01-31) Let S C R" be a Jordan measurable set. Let f be a bounded real valued function on S. Show by definition that if f is integrable on S, then f is integrable on So and | fav = |...

3 To what extent do you think that being deliberately undercharged is different from other forms of preferential treatment, such as serving you in front of other waiting customers? 4 Does the fact...

12-42. Let {X1, . . . ,Xn} depict a set of sample random variables taken from the (gamma) probability density function f (x; 0, ) = 1 (0)0 x01 ex/ , x 0; 0, > 0. Determine the most powerful test of...

10-12. Let {X1,X2, . . . ,Xn} depict a set of sample random variables drawn from the probability density function f (x; ) = -x1, 0 0; 0 elsewhere. Find a consistent estimator for .

What is the reporting objective of the special treatment given to discontinued operations?

How much time does your employer give you to read about current events related to your job?

answer using 6 th field - forensic and criminal justice. also attach the journal / article that you found ( for reference ) . it should be only about criminal and forensics, other fields cannot be...

Lease Classification, Considering Firm Guidance (Issues Memo) Facts: On 1/1/20X1, Investor, Inc. (Lessee") signed a Lease Agreement with Developer Inc. (Landlord") to lease Landlord's newly...

If a wave propagating in z-direction and incident on the air-glass interface at z = 0, plot the E field (amplitudes only) in the yz plane (plane of incidence) for: a. TE incidence b. TM incidence...

An asynchronous AC motor with three-phase Y-connected 460V, 800-rpm, 60-Hz, 8-pole, has parameters: Rs=0.5 2, R=0.3 , Xs = 0.8 2, X = 1.2 2, and Xm = 20 Q respectively. Apply the approximate...

Find the order of convergance of the following fixed-point iterative method (a is a constant): Xn+1 =2 x -ax2

49. Olivia and Tatiana form Jen Co. in 2018. Olivia contributed services worth $24,000 and property worth $1,000 and Tatiana contributed property worth $25,000. Each received 25 shares of Jen Co. Is...

Respond to: Understanding the budget process and requirements will help the agency grow and acquire the appropriate equipment and plan financially.

Let f be an extended real-valued function defined on a measurable set D CR. (a) Show that if {x D: f(x)

Could someone please check my work Let D be a nonempty set and suppose that f : D - R and g: D - R. Define the function f + g: D -> R by (f + g)(2) = f(2) + g(2) . 3. Find an example to show that...

(4) (10 pts.) Let S = A = [0, 1]. Define f : S x A - R and y : A - 25 by f(x, a) = Va for (x, a) E S x A and y(a) = [0, va] for a E A. Let y* (a) be the set of maximizers of f (, a) on ya), and f*(a)...

Let f be an extended real-valued measurable function on a measurable set D. For M, M R, M M, let the truncation of f at M and My be defined by [M g(x)=f(x) M Show that g is measurable on D. if f(x)...

Let (fn ne N) and f be an extended real-valued measurable functions on a set DCR such that limn- fn = f on D. Then for every a ER measurable prove that: (i) {x D: f(x) > a} a} (ii) n {x D: f(x)

1. A ship leaves port and travels south at 30 mi/hr. At the same time another boat which is 60 miles due east of the port, approaching the port to dock, and traveling at a rate of 40 mi/hr. After...