Let ((X, mathscr{A})) be a measurable space and assume that (mu: mathscr{A} ightarrow[0, infty]) finitely additive and

Question:

Let $(X, \mathscr{A})$ be a measurable space and assume that $\mu: \mathscr{A} ightarrow[0, \infty]$ finitely additive and $\sigma$-subadditive. Show that $\mu$ is $\sigma$-additive.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

See More Books

Question Posted: Jan 23, 2024 10:00 AM

See More Questions

Let $(X, \mathscr{A}, \mu)$ be a $\sigma$-finite measure space and assume that $\mathscr{A}$ is generated by a Boolean algebra $\mathscr{G}$, i.e. a family of subsets of $X$ which is stable...
Let V be a vector space and assume that the maps f1, f2: V R1 are linear. (a) Define a map F: V R2 whose component functions are the given linear ones. Show that F is linear. (b) Does the converse...
(Continuation of Problem 6.3) Consider on $\mathbb{R}$ the $\sigma$-algebra $\Sigma$ of all Borel sets which are symmetric w.r.t. the origin. Set \(A^{+}:=A \cap[0, \infty), A^{-}:=(-\infty, 0]...
Models that pertain to the distribution of a resource within supply chains are often referred to as networks. Distribution among these networks is key to the success of a business while also keeping...
The energy consumption associated with a home water heater has two components: (i) the energy that must be supplied to bring the temperature of groundwater to the heater storage temperature, as it is...
Some past and current civilizations, believing that interest should not be charged, passed usury laws forbidding it. What are the private and social benefits or costs of allowing interest to be...
What is the difference between a predator and a situational (accidental) fraudster?
Bolero Company holds 80 percent of the common stock of Rivera, Inc., and 40 percent of this subsidiarys convertible bonds. The following consolidated financial statements are for 2014 and 2015:...
1. Create a demand graph using the following table of values: PRICE QUANTITY 500 10 20 450 30 400 40 350 50 300 60 250 70 200 2. Create a supply graph using the following table of values: PRICE...
Let $(X, \mathscr{A}, \mu)$ be a measure space and $F \in \mathscr{A}$. Show that $\mathscr{A} i A \mapsto \mu(A \cap F)$ defines a measure.
Find a measure $\mu$ on $(\mathbb{R}, \mathscr{B}(\mathbb{R}))$ which is $\sigma$-finite but assigns to every interval $[a, b)$ with $b-a>2$ finite mass.
Live Nation operates music venues, provides management services to music artists, and promotes more than 35,000 shows and 100 festivals in 40 countries annually. The company acquired House of Blues,...
What are the mechanisms underlying protein-ligand interactions, and how do they contribute to the specificity and affinity of binding?
Johnny Rocket can run 300 meters in 100 seconds. If his speed remains constant, how far could he run in 545 seconds? Round to one decimal place. meters
What is the role of stakeholder engagement and collaboration in planning processes? Additionally, how does the importance of building consensus, managing conflicts, and fostering shared ownership and...
Question 1 Share Repurchases in Perfect Capital MarketsABCCompany hasno debt anda market capitalization of $1.5 billion and 35million shares outstanding. It plans to distribute $65 million to its...
A $90,000 reverse mortgage is for 10 years at 8% interest rate where payments are made annually at the beginning of each year. What is the ending balance on this loan in year 2?
Various Time Value Situations Answer each of these unrelated questions. (a) On January 1, 2008, Aaron Brown Corporation sold a building that cost $250,000 and that had accumulated depreciation of...
The graph of the sequence whose general term is an = n - 1 is which of the following? [8.1] A. B. TITTT 3-2-1 23.45 2.3.4
The proof of Theorem 10.3 actually shows, that almost all Brownian paths are nowhere Lipschitz continuous. Modify the argument of this proof to show that almost all Brownian paths are nowhere Hlder...
Show that for $\alpha \in(0,1)$ the function $Z \mapsto \mathbb{E}\left(|Z|^{\alpha}ight)$ is subadditive and complete the argument in the proof of Theorem 10.1 for this case. Data From Theorem...
Prove that in $\mathbb{R}^{n}$ all $\ell^{p}$-norms $(1 \leqslant p \leqslant \infty)$ are equivalent: \[\max _{1 \leqslant j \leqslant n}\left|x_{j}ight|...
CatManDoo sold 4,500 bags of kitty litter during the month of June at a price of $10/bag. The company offers a full refund to unsatisfied customers for any product returned within 30 days from the...
Discuss the relationship between formal training and development, informal learning, and knowledge management. How are they related to learning and creating a learning organization?
What comprehensive strategies and methodologies do you employ to effectively distribute and assign responsibilities among team members, ensuring optimal task allocation, synergy, and productivity...

Let ((X, mathscr{A})) be a measurable space and assume that (mu: mathscr{A} ightarrow[0, infty]) finitely additive and

Question:

Step by Step Answer:

Finite additivity implies monotonicity AC B BAU ...View the full answer

Measures Integrals And Martingales

Students also viewed these Business questions