07-02. Measure theory and probability - The measure theoretic probability model.

This video introduces the first important concepts of measure theory: sigma-algebras, Borel sets, measurable spaces, measurable functions, positive measures and the Lebesgue measure. Then we explain how Kolmogorov reinterpreted these concepts from the point of view of probability, which gave rise to modern probability theory. This is Section 1.2 of my Stochastic Modeling book.

[jkid]

For as opaque as this really ought to be, your understanding and presentation makes it seem all so clear. Much love!

[keyvanfardi]

Thank you Professor.
I love your accent.

[jlo]

So glad I found this channel!!! Thanks Prof Launchier!! :D

[qiaohuizhou]

8:30 omega is typically a topological space that characterized by open set

[HHY]

Your book and vedios are really fantastic. I am considering using you book as the materials for part of my mathematical economics courses. I am wondering is the solutions of your book available for instructors? Thanks!

[mrahman]

Professor, in the definition of positive measure, is it required to have any additional condition such as mu(empty set) = 0?

[danielkrupah]

This could be super, but the English speaking is the problem. Hard to hear clearly.