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

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

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

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

Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory.

I was taught undergraduate probability theory by… 198 more words

**F**ollowing 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

<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

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