Question: Let (X, M, p) be a measure space and let f be a nonnegative measurable function. If A E M and 4(A) = 0

Let (X, M, p) be a measure space and let f be

Let (X, M, p) be a measure space and let f be a nonnegative measurable function. If A E M and 4(A) = 0 them show that SA fdu = 0.

Step by Step Solution

★★★★★

3.51 Rating (151 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that intA f dmu 0 given that muA 0 and f is a nonnegative measurable function we can proceed ... 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 Mathematics Questions!

Q:

Let f be a nonnegative continuous function on [0,1]. (a) Show that (b) Use part (a) to evaluate xf(sin x) dx = (n/2) | f(sin x) dx. x sin x cos x ax.

Q:

Let f be a nonnegative continuous function defined on 0 ( x Show that (a) If limx( f(x) exists it must be 0; (b) It is possible that limx( f(x) does not exist. Roa f(x) dx

Q:

Let X be a nonnegative r.v. Then: (i) Use the Fubini Theorem to show that (ii) Apply this result in case the d.f. of X is F(x) = 1 -e-(x for x ( 0 and 0 for x 0); or F(x) = 0 for x EX = P(X > t)dt.

Q:

1. Let (X, M, u) be a measure space and suppose that { En } is a sequence of measurable set such that X = U. En and En C En+1, for all n E N. Let f : X - R be a measurable function such that f |f|du

Q:

Consider the measure space ( X , , ) , ( X ) . Suppose that f , f n , g , g n : X R , n N are measurable , i.e, a R : f 1 ( { a } ) ,where isa algebra . Prove that a) ( { x X f ( x ) > n } ) 0 , n ....

Q:

Ace Delivery purchased a new food delivery truck on 4/30/2019 for $125,000. Other costs included: sales tax $8,000 and installation of a refrigeration unit $12,000. Ace estimates the following:...

Q:

Let \((X, \mathscr{A}, \mu)\) be a measure space and let \(T: X ightarrow X\) be a bijective measurable map whose inverse \(T^{-1}: X ightarrow X\) is again measurable. Show that for every \(f \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:

Kernels. Let \((X, \mathscr{A}, \mu)\) be a measure space. A map \(N: X \times \mathscr{A} ightarrow[0, \infty]\) is called a kernel if \[ \begin{array}{rlrl} A & \mapsto N(x, A) & & \text { is a...

Q:

Can you challenge Piagets belief that infants construct all mental representations out of sensorimotor activity?

Q:

A double-wall heat exchanger is used to transfer heat between liquids flowing through semicircular copper tubes. Each tube has a wall thickness of t = 3 mm and an inner radius of r; = 20 mm. and good...

Q:

Graber Corporation common stock has a beta of 1.15. If the risk-free rate is 3.5 percent and the expected market return is 11 percent, what is the firm's cost of equity?

Q:

Find the general indefinite integral. ( Remember the constant of integration. ) ( 4 x ^ 3 + 6 x + 3 ) dx

Q:

Given that the probability that A occurs is .3, the probability that B does not occur is .6, and the probability that either A or B occurs is .5, find: (a) The probability that A does not occur. (b)...

Q:

From the probabilities shown in this Venn diagram, determine the probabilities of the following events. (a) A does not occur. b) A occurs and B does not occur. (c) Exactly one of the events A and B...

Q:

A local bookstore intended to award three gift certificates in the amounts $100, $50, and $25 to the first, second, and third customer to identify a mystery author. Unfortunately, a careless clerk in...

Q:

A plant geneticist crosses two parent strains, each with gene pairs of type aA. An offspring receives one gene from each parent. (a) Construct the sample space for the genetic type of the offspring....

Q:

Fifteen persons reporting to a Red Cross center one day are typed for blood, and the following counts are found: If one person is randomly selected, what is the probability that this person's blood...

Q:

Consider the "Clothing" and "Jewelry and Watches" in US. Are the price elasticities of demand in the short run and long run what you would expect? Explain. Also explain why the demand for "Clothing"...

Q:

Let \((X, \mathscr{A}, \mu)\) be a measure space and let \(\mathscr{G} \subset \mathscr{A}\) be a sub- \(\sigma\)-algebra such that \(\left.\muight|_{\mathscr{G}}\) is \(\sigma\)-finite. Let \(p, q...

Q:

Let \((X, \mathscr{A}, \mu)\) be a finite measure space. Show that every measurable \(u \geqslant 0\) with \(\int \exp (h u(x)) \mu(d x) 0\) is in \(\mathcal{L}^{p}(\mu)\) for every \(p \geqslant...

Q:

a. Example 13-1: Batch Reactor with an Exothermic Reaction Wolfram 1. Adiabatic Case: Use Wolfram to see whether you can find a trajectory that is ready to ignite and whose trajectory looks like a...

Q:

Adding energy prices to the AS curve In this problem, we incorporate the price of energy inputs (e.g. oil) explicitly into the AS curve. Suppose the price-setting equation is given by P = (1 + )Wa PE...

Q:

1 point Consider the following statement Everyone likes playing games For the following questions Let X people P x be the predicate x likes playing games Write the statement in quantified form OA...

Q:

Consider the following program in Scheme: What does this programprint? What would it print if Scheme used dynamic scoping and shallow binding? Dynamic scoping and deep binding? Explain your answers....