Intereting Posts

Find the slope of a line given a point and an angle
Show that $d/dx (a^x) = a^x\ln a$.
Use two solutions to a high order linear homogeneous differential equation with constant coefficients to say something about the order of the DE
If point is zero-dimensional, how can it form a finite one dimensional line?
If $n$ is a positive integer, Prove that $\frac1{2^2}+\frac1{3^2}+\dotsb+\frac1{n^2}\lt\frac{2329}{3600}.$
Theorem on natural density
Can anybody explain about real linear space and complex linear space?
Is this a valid partial fraction decomposition?
Motivation behind the definition of Prime Ideal
Convergence of the integral $\int_0^{\pi/2}\ln(\cos(x))dx$
Plotting graphs using numerical/mathematica method
Combinatorial Interpretation of a Certain Product of Factorials
Writing up a rigorous solution for finding a basis for the $n \times n$ symmetric matrices.
How to write down formally number of occurences?
Limit of argz and r

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

- Expectation conditioned on an event and a sigma algebra
- If $(X_n)$ is i.i.d. and $ \frac1n\sum\limits_{k=1}^{n} {X_k}\to Y$ almost surely then $X_1$ is integrable (converse of SLLN)
- Find the expectiation of $\displaystyle\frac{X_1 + \dots + X_m}{X_1 + \dots + X_n}$
- Is the set of all probability measures weak*-closed?
- Basic Geometric intuition, context is undergraduate mathematics
- Random walk in the plane
- Dunford-Pettis Theorem
- what are the sample spaces when talking about continuous random variables
- Random Variable Inequality
- The Supremum and Infimum of a sequence of measurable functions is measurable

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.

- Resource request: history of and interconnections between math and physics
- Show that $89|(2^{44})-1$
- Characterize all topological spaces with a certain cancellation rule
- Isomorphism of Banach spaces implies isomorphism of duals?
- Contradiction achieved with the Pettis Measurability Theorem?
- Subgroups of $S_4$ isomorphic to $S_3$ and $S_2$?
- Origin of the dot and cross product?
- How prove $(1-\sum_{i=1}^{n}a^3_{i})^{1/3}\cdot (1-\sum_{i=1}^{n}b^3_{i})^{1/3}\ge 1-\sum_{i=1}^{n}a_{i}b_{i}-\sum_{i=1}^{n}|a_{i}-b_{i}|$
- Self-teaching myself math from pre-calc and beyond.
- The product of two Riemann integrable functions is integrable
- Prove a square is homeomorphic to a circle
- Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
- What are zero divisors used for?
- If $\lim a_n = L$, then $\lim s_n = L$
- What is the number of invertible $n\times n$ matrices in $\operatorname{GL}_n(F)$?