Tags » Sigma-algebra

Probability Theory: Homework 1

Exercises, due Wed Sept 3.

From Jacod and Protter, problems 2.6, 2.7, 2.10 and 2.14.

2.6 Let be a -algebra of subsets of and let . 57 more words

Probability Assignments

Prove that if a collection M is closed under compliments and countable unions of disjoint sets then M is a sigma algebra.

Let be a set and be a non-empty collection of subsets of .  Prove that if is closed under compliments and countable unions of disjoint sets then M is a -algebra. 142 more words

Real Analysis

A Walk in the Park

A runner comes towards me and I concentrate on her face.

… making it a countable union of countable sets and therefore countable Q.E.D.

I wish I knew what that meant. 407 more words

Stories

Buffon versus Bertrand in R

Following my earlier post on Buffon’s needle and Bertrand’s paradox, above are four outcomes corresponding to four different generations (among many) of the needle locations. 487 more words

Statistics

Interesting discourse On Probability and Sigma Algebra

<ebook on Sigma Algebra>

I found this VERY descriptive and it answers some of the most important points on smallest and largest sigma algebra .  21 more words

Resources

245A, Notes 3: Integration on abstract measure spaces, and the convergence theorems

Thus far, we have only focused on measure and integration theory in the context of Euclidean spaces . Now, we will work in a more abstract and general setting, in which the Euclidean space is replaced by a more general space . 8,733 more words

Math.CA