Purchase Solution

Bore-Cantelli Lemma

Not what you're looking for?

Ask Custom Question

Let {f_n} be a sequence of measurable functions on [0,1] with |f_n (x)| < infinity for a.e x. Show that there exists a sequence c_n of positive real numbers such that
f_n (x) / c_n -------> 0 a.e.x.

Hint: Pick c_n such that m ({x : |f_n (x) / c_n| > 1/n} ) < 2^(-n), and apply the Bore-Cantelli Lemma.

Purchase this Solution

Solution Summary

Bore-Cantelli Lemma is integrated into the solution..

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

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

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.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability