# Mathematical Foundations of Probability Theory

@article{Lo2018MathematicalFO, title={Mathematical Foundations of Probability Theory}, author={Gane Samb Lo}, journal={arXiv: Probability}, year={2018} }

In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited theory. The book might have assigned the title : From Measure Theory and Integration to Probability Theory. The fundamental aspects of Probability Theory, as described by the keywords and phrases below, are presented, not from experiences as in the book \textit{A…

## 7 Citations

### Weak Convergence (IIA) - Functional and Random Aspects of the Univariate Extreme Value Theory

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The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In…

### Finiteness of Record values and Alternative Asymptotic Theory of Records with Atom Endpoints

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Asymptotic theories on record values and times, including central limit theorems, make sense only if the sequence of records values (and of record times) is infinite. If not, such theories could not…

### A Detailed and Direct Proof of Skorohod-Wichura's Theorem

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The representation Skorohod theorem of weak convergence of random variables on a metric space goes back to Skorohod (1956) in the case where the metric space is the class of real-valued functions…

### Study on A Direct Construction of the Standard Brownian Motion

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In this note, we combine the two approaches of Billingsley (1998) and Csőrgő and Revesz (1980), to provide a detailed sequential and descriptive for creating s standard Brownian motion, from a…

### Suppressing information storage in a structured thermal bath

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Quantum systems interacting with environments tend to have their information lost from transmission through the correlations generated with the degrees of freedom of the environment. For situations…

### On the Glivenko-Cantelli theorem for the functional empirical process using associated sequences

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Using a general strong law of large number proved by Sangare and Lo in \cite% {sanglo} and the entropy numbers, we provide a functional Glivenko-Cantelli theorem for arbitrary random variables (rv's).

### On the Law of Large Numbers for Nonlinear Mean Random Variables

- MathematicsRussian Mathematics
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We consider variants of the law of large numbers with respect to the average power, average geometric and mean harmonic systems of random variables and establish various forms of convergence of the…

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