Intereting Posts

Is there any formula for number of divisors of $a \times b$?
Linearly independent functionals
Principal ultrafilter and free filter
Question about quadratic twists of elliptic curves
How to find basis for intersection of two vector spaces in $\mathbb{R}^n$
$\epsilon$-$\delta$ limit proof, $\lim_{x \to 2} \frac{x^{2}-2x+9}{x+1}$
How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
Strange consequences of Axiom of Choice in Zermelo set theory
Prove that $\overline{A \cup B} = \overline A\cup \overline B$.
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
Telling which sum is greater, the odd or even powers of a Poisson random variable
Why the axioms for a topological space are those axioms?
If $g \circ f$ is the identity function, then which of $f$ and $g$ is onto and which is one-to-one?
$\frac{a^{2}+b^{2}}{1+ab}$ is a perfect square whenever it is an integer
So-called Artin-Schreier Extension

I’m looking for a clear way to learn measure theoretic probability theory. Any suggestions?

- Approximation on partitions in $L^2(\times \Omega)$
- How often was the most frequent coupon chosen?
- Limit of $L^p$ norm
- Result and proof on the conditional expectation of the product of two random variables
- A pathological example of a differentiable function whose derivative is not integrable
- The “true” domain of random variables
- Given a joint characteristic function, find $P(X<Y)$
- Bounded stopping times and martingales
- Questions on Kolmogorov Zero-One Law Proof in Williams
- About measure theoretic interior and boundary

I would recommend Erhan Çinlar’s *Probability and Stochastics* (Amazon link).

*Probability With Martingales* by David Williams is a very enjoyable book.

You can try the lecture notes here: http://www.statslab.cam.ac.uk/~beresty/teach.html

They’re very good.

Noel Vaillant’s online Probability Tutorials are an excellent introduction to the real analysis, general topology and measure theory foundations of probability theory.

Kallenberg – Foundations of Modern Probability.

Probability and Measure, P. Billingsley.

A really comprehensive, easy to read book would be “An Introduction to measure and probability” by J.C Taylor (Amazon).

Lots of examples, exercises, and really nice geometric view of conditional expectation via Hilbert spaces.

- Do eigenvalues of a linear transformation over an infinite dimensional vector space appear in conjugate pairs?
- If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.
- Minimum value of $\cos x+\cos y+\cos(x-y)$
- Prove $\left(\frac{2}{5}\right)^{\frac{2}{5}}<\ln{2}$
- Proving that the set of limit points of a set is closed
- What does it mean to induce a topology?
- Why is negative times negative = positive?
- Möbius strip and $\mathscr O(-1)$. Or $\mathscr O(1)$?
- How to estimate the size of the neighborhoods in the Inverse Function Theorem
- Can the product of two non invertible elements in a ring be invertible?
- Eigenvectors question
- Possible ways to do stability analysis of non-linear, three-dimensional Differential Equations
- Proof for an integral identity
- Why is this series of square root of twos equal $\pi$?
- Simplifying radicals inside radicals: $\sqrt{24+8\sqrt{5}}$