Question: Let (X) be an arbitrary set and (mathscr{F} subset mathscr{P}(X)). Show that [sigma(mathscr{F})=bigcup{sigma(mathscr{C}): mathscr{C} subset mathscr{F} text { countable sub-family }}]

Let \(X\) be an arbitrary set and \(\mathscr{F} \subset \mathscr{P}(X)\). Show that

\[\sigma(\mathscr{F})=\bigcup\{\sigma(\mathscr{C}): \mathscr{C} \subset \mathscr{F} \text { countable sub-family }\}\]

Step by Step Solution

★★★★★

3.41 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Write o 6 C CF C is a countable subfamily If C C F we get o 6 CoF and so C G F Conversely it ... 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:

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...

Q:

How do social norms contribute to the maintenance of social order and stability, while also serving as mechanisms for social control and the enforcement of conformity?

Q:

Imagine we have the data frame below and we have named it "df" in R. worker wage state 1 11 2 9 3 20 4 40 5 5 CA CA AZ AZ OR In the R console I type: mean(wage) But receive the error "object 'wage'...

Q:

Monotone classes (2). Recall from Problem 3.14 that a monotone class \(\mathscr{M} \subset \mathscr{P}(X)\) is a family which contains \(X\) and is stable under countable unions of increasing sets...

Q:

Regularity on Polish spaces. A Polish space X X is a complete metric space which has a countable dense subset D X D X . Let be a finite measure on ( X , B ( X ) ) ( X , B ( X ) ) . Then is...

Q:

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Q:

in here P(A) is power set of(A) 1.Prove that A B iff P (A) P (B). 2. Prove that for any set A, A = P (A). 3. Suppose {Ai | i I} and {Bi | i I} are indexed families of sets. (a) Prove that iI (Ai...

Q:

I need help with this problem please. I did it but it was false, I attached the feedback and the example of 3.7.5. Consider the function f(x) = ^3 for x ? R and -2 20. Consider the function f(x) = x...

Q:

Some problems about cuts. Doesn't need a formal proof, just want some ideas about how to proof these statement. Cuts are sometimes dened as subsets of the edges of the graph, instead of as partitions...

Q:

f x x Let x be any arbitrary element of R then Right hand limit at x x lim f x lim f x h X X Institute of Lifelong Learning University of Delhi lim x h 40 lim x h 2xh 0 0 lim f x x X X Left hand...

Q:

Research "Leadership Success and Failure," and write a paper on the topic. Many leaders across industry, government, entertainment and humanitarianism have discussed their success and have shared...

Q:

Interpret each of the three ways of writing the condition for equilibrium income in the simple Keynesian model [equations (2), (5)., and (6)]. Explain why the three ways are equivalent.

Q:

1 9 Anume you labe but a car loan of $ 9 , 0 0 0 that calls for 3 6 montly phyments of $ 1 4 0 each 1 8 2 moln e . What is the A / Pe of the loan? Note: De not ehond intermediate caloviations. Inter...

Q:

2. Give an example of strategic planning and tactical planning.

Q:

Let \(\left(P_{t}ight)_{t \geqslant 0}\) and \(\left(T_{t}ight)_{t \geqslant 0}\) be two Feller semigroups with generators \((A, \mathfrak{D}(A))\), resp. \((B, \mathfrak{D}(B))\). a) If...

Q:

Let \(A, B \in \mathbb{R}^{d \times d}\) and set \(P_{t}:=\exp (t A):=\sum_{j=0}^{\infty}(t A)^{j} / j\) !. a) Show that \(P_{t}\) is a strongly continuous semigroup. Is it contractive? b) Show that...

Q:

Show that \(\mathcal{C}_{\infty}:=\left\{u: \mathbb{R}^{d} ightarrow \mathbb{R}ight.\) : continuous and \(\left.\lim _{|x| ightarrow \infty} u(x)=0ight\}\) equipped with the uniform topology is a...

Q:

High Road Transport has a current stock price of $5.60. For the past year, the company had net income of $287,400, total equity of $992,300, sales of $1,511,000, and 1,500,000 shares outstanding....

Q:

Syzslak Incorporated entered two transactions, as follows: 1. March 1, purchased equipment paying $20,000 at the date of purchase and signing a noninterest-bearing note requiring the balance to be...

Q:

It is January 1, 2016. Starting today, you plan to invest $5,000 at the beginning of every quarter for fifteen years into a pension fund that will deliver an effective annual return of 7.5% net of...