# Questions tagged [measure-theory]

A field of mathematics concerning measures, which are functions mapping sets to real numbers that generalize the idea of area and volume. Measure theory underlies modern treatments of probability. Questions about measure theory with a weak connection to probability or statistics may be more suitable for math.stackexchange.com than this site.

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### Probability Measure for Continuous Random Variable

Say a continuous random variable $X \in \mathbb{R}$ has a probability density function (p.d.f.). Is it correct that, change the probability measure $\Rightarrow$ define a new p.d.f. for X ? In other ...
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### Probability Assigned to Distance between Two People Random Walking in a Room [closed]

In a scenario where there are two people in the rooms next to each other randomly walking in a room I want to know if we can compute PDF of distance between the two people. So the way I tried to ...
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I'm searching for a book who treat GLM in a formal way, with a measure theoretic approach. Someone could help me? i try to be more specific Suppose $(\Omega,\mathcal{F},\mathbb{P})$ is a probability ...
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### Lots of modes of convergence for random variables but why is there nothing on convergence of probability density functions?

There are numerous modes of convergence for random variables. But why do I never read anything about convergence of probability density functions? It seems like this would also be an important notion ...
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### Likelihood function when there is no common dominating measure?

When we have a statistical model $\{ P_\theta, \theta\in\Theta\}$ on some common probability space, usually we define "the" likelihood function $L(\theta)$ via a Radon-Nikodym derivative ...
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### Different modes of stating probability law [duplicate]

I met two versions of expressing induced probability measure on $\mathbb{R}^n$ of n-dimensional random vector $\mathbf{X} = (X_1, \ldots, X_n)$ (probability law, probability distribution) defined on ...
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