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Category Archives: Measure Theory
Derivatives and Integrals, Part 2
Near the end of my last post I commented on how I would like to prove the interchanging of the integral using only the fact that . As it turns out it’s not possible, if this is our only assumption. … Continue reading
Posted in Measure Theory
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Derivatives and Integrals
In the last post I stated the following as a theorem. If then . I was trying to prove this earlier and found that I needed a different set of assumptions. I’m not saying that the above is wrong (though … Continue reading
Posted in Measure Theory
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Conditional Expectation
In the previous post I touched on the expected value of a random variable, and what it means for a set of random variables (or events) to be independent. Before proceeding any further I’ll give a few examples and definitions. … Continue reading
Posted in Expected value and Variance, Measure Theory
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On Convergence
In the previous post I mentioned two modes of convergence, in probability and surely. It should be noted that neither implies the other. Example 1: Convergence almost surely doesn’t imply convergence in probability Let where . Then we have that … Continue reading
Posted in Measure Theory
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Introduction
Hello and welcome to my probability blog. The material in future post would be considered by most to be at a graduate level. Though this shouldn’t discourage you if you are not a graduate student, I am going to try … Continue reading
Posted in Measure Theory
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