Let 1, n be finite measure on ((, A) and set 1 n (in the sense that (A) (ni 1 i(A), A ( A) Then show that is also finite ...

For n 2 let 1 and 2 be finite and let A 1 1 A 1 2 and A 2 1 A 2 2 be the ass ...

Let 1,...n be -finite measure on ((, A) and set = 1 + ... + n

Question:

Let μ1,...μn be σ-finite measure on ((, A) and set μ = μ1 + ... + μn (in the sense that μ (A) = (ni=1 μi(A), A ( A). Then show that μ is also σ-finite.

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

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Measure Theoretic Probability

ISBN: 978-0128000427

2nd edition

Authors: George G. Roussas

See More Books

Question Posted: Mar 25, 2016 03:21 AM

See More Questions

Consider the (Ï-finite) measure space ((, A, Î¼), and let {Ai, i = 1, 2,....} be a (measurable) partition of (. For each i, define the measure Î¼i by: Î¼i...
Let be a -finite measure and let be a nonnegative -additive and finite function, both defined on the measurable space ((, A). Then show that < < is equivalent to the following: for every ( > 0,...
Let Xk, k = 1, 2, 3¦ be a sequence of IID random variables with finite mean, , and let Sn be the sequence of sample means, (a) Show that the characteristic function of Sn can be written as (b)...
Find all conjugates in C of the given number over the given field. 1+2 over Q
A clients purchasing system ends with the recording of a liability and its eventual payment. Which of the following best describes auditors primary concern with respect to liabilities resulting from...
Evaluate the indefinite integral, using substitution if necessary. Sx x3x dx
Match the following concepts: goal, process, function, scenario, business system, information system, grocery store, check-out system, actors, role.
Sometimes, the root cause of a variance requires that variance analysis be performed in both hours and dollars. It is possible that calculating the variances in both hours and dollars is the only way...
Lindberg Company uses a normal job-order costing system. There are two departments, Assembly and Finishing, through which most jobs pass. Selected budgeted and actual data for the past year follow:...
Find a (real) general solution. State which rule you are using. Show each step of your work. 10y" + 50y' + 57.6y = cos x
Consider the measure space ((, B, Î¼) where Î¼ (finite interval) Then, by means of an example, show that Fc need not be left-continuous. c + ((0, x]) x > 0, c ((x, 0]) x <...
In the probability space ((, A, P), show that (i) P[(A ( Bc) Ac ( B)] = P(A) + P(B) - 2P (A ( B). (ii) P(A1 ( ... ( An) ( (ni=1 P(Ai) - (n - 1).
Discuss some of the managerial challenges that complementary products present.
An accountant has described cost allocations to joint products as a necessary evil? Comment.
Explain the meaning of batch costing. How does such a costing differ from job costing?
Compare the weighted average method with the FIFO method in calculating unit costs.
Under what circumstances are identical results obtained under weighted average and FIFO process costing?
A firm is engaged in manufacturing jobs of long duration. Examine the detailed procedure suitable for costing purposes.
How does the Disney Company use Alderfers ERG theory of motivation to motivate its workforce?
A business had revenues of $280,000 and operating expenses of $315,000. Did the business (a) Incur a net loss (b) Realize net income?
It is suspected that some of the totes containing chemicals purchased from a supplier exceed the moisture content target. Samples from 30 totes are to be tested for moisture content. Assume that the...
Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. Determine the length of an interval of time such that the probability that no messages arrive...
Flaws occur in the interior of plastic used for automobiles according to a Poisson distribution with a mean of 0.02 flaw per panel. (a) If 50 panels are inspected, what is the probability that there...
A taxpayer disposed a part of asset for 100,000 SR in cash. The taxpayer purchased that asset for 90,000 SR 5 years ago but the market value of the complete assets was as follows: Part disposed...
A company maintains debt/equity ratio of 0.6. The flotation cost of equity is 12% and flotation cost of debt it is 6%. The firm is considering a new project which will require $5 million in external...
Flight Caf prepares in-flight meals for airlines in its kitchen located next to a local airport. The company's planning budget for July appears below: Flight Caf Planning Budget For the Month Ended...

Let 1,...n be -finite measure on ((, A) and set = 1 + ... + n

Question:

Step by Step Answer:

For n 2 let 1 and 2 be finite and let A 1 1 A 1 2 and A 2 1 A 2 2 be the ass...View the full answer

An Introduction to Measure Theoretic Probability

Students also viewed these Statistics questions