Purchase Solution

Sigma algebras, measure spaces, rectangles, and cylinders

Not what you're looking for?

Ask Custom Question

Let (Omega_1, F_1, P_1) and (Omega_2, F_2, P_2) be the following measure spaces:

Omega_1 = {a, b}, F_1 is the sigma algebra of all subsets of Omega_1, and P_1 is a measure on Omega_1.

Omega_2 = {c, d}, F_2 is the sigma algebra of all subsets of Omega_2, and P_2 is a measure on Omega_2.

Determine the makeup of the set C of cylinders of Omega_1 and the set R of rectangles of Omega_2, and show that C is a subset of R.

Attachments
Purchase this Solution
Solution Summary

The set of rectangles and the set of cylinders for the given pair of measure spaces is determined (in detail), and it is shown that the set of cylinders is contained in the set of rectangles.

Solution Preview

Let Omega_1 = {a, b} and Omega_2 = {c, d}.

By definition of the sigma algebra of all subsets of Omega_1,

F_1 = {empty set, {a}, {b}, {a,b}}

Similarly, by definition of the sigma algebra of all ...

Solution provided by:
Georgia Martin, PhD
Education
  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
Recent Feedback
  • "Thanks for your assistance. "
  • "Thank you. I understand now."
  • "Super - Thank You"
  • "Very clear. I appreciate your help. Thank you."
  • "Great. thank you so much!"
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Real Analysis Topology and Sigma-Algebra

    Sigma-algebras are investigated. The solution is detailed and well presented.

  • Problem on X bar chart-UCL, LCL

    Determine the centerline and the upper and lower control limits for a 3-sigma mean control chart in which each sample consists of 4 cylinders Please see attached for explanation.

  • Integrals : Riemann Sum with Diagrams

    I can't make the Sigma symbol on the computer, so I used the word "Sigma" instead. For (c), n is above the Sigma symbol and i=1 is below it.

  • Euclidean and Non-Euclidean geometry

    It can be proved that rectangles do not exist by taking a rectangle and dividing it into two triangles from one corner to another, because in hyperbolic geometry rectangles are made up of two triangles.

  • Robot Welder: Statistic

    Determine the centerline and the upper and lower control limits for a 3-sigma mean control chart in which each sample consists of 4 cylinders. 20.42 Samples of 12-volt batteries are taken at 30 minutes intervals during a production run.

  • Free Boolean Algebra

    Since the categories of Boolean algebras and of Boolean rings are isomorphic, and the corresponding isomorphism F:BoolAlg-->BoolRings is compatible with the above-mentioned forgetful functors, F gives an isomorphism of their left adjoints.

  • Another Measurer in Java

    @param anObject the object to be measured @return the measure */ double measure(Object anObject); }. Please see the attachment. The solution uses a measurer to find several rectangles' maximum perimeter and average perimeter.

  • Six Sigma

    In other words, Six Sigma simply means a measure of quality that strives for near perfection.

  • Six Sigma and Lean

    The DMAIC of the Six Sigma methodologies is applicable to manufacturing and production side of the service. It has these stages of Define, Measure, Analyze, improve, and control.

View More Related Solutions