Let (S) be any set and (mathscr{E}) be a family of subsets of (S). Show that [sigma(mathscr{E})=bigcup{sigma(mathscr{C}):

Question:

Let $S$ be any set and $\mathscr{E}$ be a family of subsets of $S$. Show that

\[\sigma(\mathscr{E})=\bigcup\{\sigma(\mathscr{C}): \mathscr{C} \subset \mathscr{E}, \mathscr{C} \text { is countable }\}\]

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

Step by Step Answer:

Related Book For book-img-for-question

Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

ISBN: 9783110741254

3rd Edition

Authors: René L. Schilling, Björn Böttcher

See More Books

Question Posted: Mar 16, 2024 11:00 PM

See More Questions

The null hypothesis is Ho:u1 = u2 and the alternative hypothesis is as specified. The data available below are from a simple random paired sample from the two populations under consideration. Use the...
Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...
PLEASE GIVE CORRECT ANSWERS Prove that the number of comparators in any sorting network is (n log n). [4 marks] (ii) What does Part (d)(i) imply in terms of the depth of any sorting network? [1 mark]...
1Describe in a simplified manner the flow of information from gene to protein
As a increases, so does the power to detect an effect. Why, then, do we restrict a from being larger than .05?
Are you aware of making assumptions about other people based on their backgrounds and appearance? Did you check those assumptions? Have your assumptions turned out to be correct, or not? What will...
Explain how managers use data-based decision making. LO.1
Cherokee Furniture Company manufactures furniture. Cherokee Furniture uses a job order cost system. Balances on April 1 from the materials ledger are as follows: Fabric ...... $ 6,140 Polyester...
You are looking at an investment that will generate $100,000 of cash flow starting in year 1, increasing annually at 3%. You can buy the property for $2,000,000 and forecast selling it at the end of...
Let $\emptyset eq E \in \mathscr{B}\left(\mathbb{R}^{d}ight)$ contain at least two elements, and $\emptyset eq I \subset[0, \infty)$ be any index set. We denote by $E^{I}$ the product space...
Show that there exists a stochastic process $\left(X_{t}ight)_{t \geqslant 0}$ such that the random variables $X_{t}$ are independent $\mathrm{N}(0, t)$ random variables. This process also...
Eclectic Ergonomics Company manufactures designer furniture. Eclectic Ergonomics uses a job order cost system. Balances on April 1 from the materials ledger are as follows:...
As the human resource manager, how would you evaluate the training needs of your staff? How can you ensure that the training you would provide is effective? What data might be used to make your...
MARYLAND CORPORATION manufactures three liquid products - Alpha, Beta and Gamma using a joint process with direct materials, direct labor and overhead totaling $560,000 per batch. In addition, the...
Three common organizational structures. Mention one organization for each organizational structure which is following a specific organizational structure. Also, provide support to your answer by...
You are a retail manager at Kitchen Nightmare, a relatively new store at the mall that sells mostly items for kitchens, like forks, oven mitts, etc.. You have been open since the fall of 2021 and...
Examine the extent to which the Department of Veteran Affairs has established any processes or procedures to ensure knowledge retention of departing employees. Why is it important to manage the...
Refer to Exercise 5.30. In fact, the researcher was more concerned about determining if the lead in the paint reduced the mean number of Type 2 fibers in skeletal muscles. Does the change in the...
Is times interest earned meaningful for utilities? Why or why not?
Compute the expected value for the geometric distribution using formula (2.2.1) and compare your calculation with those.
Does the fact that E{X} has a moderate value, mean that X cannot assume big values? Let us consider a r.v. for large n. Such a r.v. may illustrate a possible future loss connected with a possibility...
In a show, you are given two closed envelopes containing positive sums of money. It is known that one envelope contains twice as much as the other. You may choose one envelope and keep the money it...
The following amounts were reported on the December 31, 2022, balance sheet: Cash $ 8,000 Land 20,000 Accounts payable 15,000 Bonds payable 120,000 Merchandise inventory 30,000 Retained earnings...
Sandhill Co. issued $ 600,000, 10-year, 8% bonds at 105. 1.Prepare the journal entry to record the sale of these bonds on January 1, 2017. (Credit account titles are automatically indented when the...
Based on the regression output (below), would you purchase this actively managed fund with a fee of 45bps ? Answer yes or no and one sentence to explain why.

Let (S) be any set and (mathscr{E}) be a family of subsets of (S). Show that [sigma(mathscr{E})=bigcup{sigma(mathscr{C}):

Question:

Step by Step Answer:

Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

Students also viewed these Business questions