Question: Prove that every function (u: mathbb{N} ightarrow mathbb{R}) on ((mathbb{N}, mathscr{P}(mathbb{N}))) is measurable.

Prove that every function \(u: \mathbb{N} ightarrow \mathbb{R}\) on \((\mathbb{N}, \mathscr{P}(\mathbb{N}))\) is measurable.

Step by Step Solution

★★★★★

3.31 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

This is actually triv... View full answer

blur-text-image
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 Measures Integrals And Martingales Questions!

Q:

Egorov's theorem. Let \((X, \mathscr{A}, \mu)\) be a finite measure space and \(f_{n}: X ightarrow \mathbb{R}, n \in \mathbb{N}\), a sequence of measurable functions. Prove the following assertions....

Q:

Show that \(x \mapsto \max \{x, 0\}\) and \(x \mapsto \min \{x, 0\}\) are continuous, and by virtue of Problem 8.7 or Example 7.3 , measurable functions from \(\mathbb{R} ightarrow \mathbb{R}\)....

Q:

Let \((X, \mathscr{A})\) be a measurable space. (i) Let \(f, g: X ightarrow \mathbb{R}\) be measurable functions. Show that for every \(A \in \mathscr{A}\) the function \(h(x):=f(x)\), if \(x \in...

Q:

Let \((X, \mathscr{A}, \mu)\) be a measure space and \(\left(u_{n}ight)_{n \in \mathbb{N}} \subset \mathcal{M}(\mathscr{A})\). (i) Let \(\left(x_{n}ight)_{n \in \mathbb{N}} \subset \mathbb{R}\). Show...

Q:

Let \(\mu\) be a finite measure on \(\left(\mathbb{R}^{n}, \mathscr{B}\left(\mathbb{R}^{n}ight)ight)\) and denote by \(\phi(\xi):=\widehat{\mu}(\xi)\) the Fourier transform (i) \(\phi\) is positive...

Q:

Lvy's continuity theorem. The steps below sketch a proof of the following theorem. Theorem (P. Lvy; continuity theorem). Let \(\left(\mu_{i}ight)_{i \in \mathbb{N}}\) be a sequence of finite measures...

Q:

.Let \((X, \mathscr{A})\) be a measurable space. (i). Let \(\mu, u\) be two measures on \((X, \mathscr{A})\). Show that the set function \(ho(A):=a \mu(A)+\) \(b u(A), A \in \mathscr{A}\), for all...

Q:

Use Theorem 21.18 for a new proof of Lvy's continuity theorem (Problem 21.3 ). (i) Show (as in Problem 21.3 ) that \(\lim _{i ightarrow \infty} \int u d \mu_{i}\) exists for all \(u \in...

Q:

Let \(\left(u_{n}ight)_{n \in \mathbb{N}}\) be a sequence of measurable functions on a \(\sigma\)-finite measure space \((X, \mathscr{A}, \mu)\) and assume that \(u_{n} \stackrel{\mu}{ightarrow} u\)....

Q:

Company S purchased 1,000 units raw materials amounting to $5,000 and used $4,500 worth for the production during the current month. The standard price for these raw materials is $5.2 per unit. How...

Q:

Here are the batting averages of the National League's Most Valuable Players from 1980 to 2000. (The New York Times Almanac 2002) {.286, .316, .281, .302, .314, .353, .290, .287, .290, .291, .301,...

Q:

62. Playbill is a magazine distributed around the country to people attending musicals and other theatrical productions. The mean annual household income for the population of Playbill readers is...

Q:

UNIT COSTS, MULTIPLE PRODUCTS, VARIANCE ANALYSIS, SERVICE SETTING The maternity wing of the city hospital has two types of patients: normal and cesarean. The standard quantities of labor and...

Q:

Greiner, Inc., a calendar year S corporation, holds no AEP. During the year, Chad, an individual Greiner shareholder, receives a cash distribution of $30,000 from the entity. Chads basis in his stock...

Q:

Holbrook, a calendar year S corporation, distributes $15,000 cash to its only shareholder, Cody, on December 31. Codys basis in his stock is $20,000, Holbrooks AAA balance is $8,000, and Holbrook...

Q:

Vogel, Inc., an S corporation for five years, distributes a tract of land held as an investment to Jamari, its majority shareholder. The land was purchased for $45,000 ten years ago and is currently...

Q:

impus Common Stock C has a standard deviation of return of 10 percent. Common Stock D has a standard deviation of return of 20 percent. The correlation coefficient between the two stocks is 0.5. If...

Q:

what network are most common type of network found in LAN.

Q:

Using client - side virtualization, how many operating systems can be running on your computer at one time?