# Linear Isometry, Radon-Nikodym Derivative and Isomorphisms

Not what you're looking for?

Let be a measurable space and let be two -finite measures defined on . Suppose and is the Radon-Nikodym derivative of with respect to . Define by Show that is a well-defined linear isometry and is an isomorphism if and only if (i.e are mutually absolutely continuous).

---

##### Purchase this Solution

##### Solution Summary

Linear Isometry, Radon-Nikodym Derivative and Isomorphisms are investigated. The solution is detailed and well presented.

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Multiplying Complex Numbers

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

##### 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.

##### Graphs and Functions

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

##### Exponential Expressions

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