Christoph Börgers

On this site, I collect brief notes about various topics in mathematics of interest to me.

Much of the material is not original. Some may be. I hope that it’s all well-written and interesting.

Abel's theorem

Acceptance-rejection sampling

Algebra of sets

Almost sure convergence

Arctangent at infinity

Bayes' Theorem

Bayesian statistics

Beta function

Binomial coefficients

Binomial series

Bohr-Mollerup theorem

Borel-Cantelli lemma

Brownian motion

Cadlag property

Caratheodory measurable

Caratheodory outer measure

Caratheodory's extension theorem

Cauchy's formula for repeated anti-differentiation

Central limit theorem

Characteristic functions

Condorcet breakdown

Convergence in distribution

Convergence in probability

Diffusion

Duverger's law

Equilibrium renewal processes

Error function

Euler's product representation of the gamma function

Euler-Mascheroni constant

Expected value

Exponential integral

Extendability condition for finitely additive measures

Extension of measures from finite additivity to countable additivity

Extreme value theory

Finitely additive measure

First passage time

Fourier transform

Fractional calculus

Frechet distributions

Gamma function

Gumbel distribution

Hegselmann-Krause model

Infinite products

Kermack-McKendrick model

Laplace transform

Laplace's rule of succession

Law of exponents

Lebesgue-Stieltjes measure

Left-right model of election outcomes

Linear algebra

Majority judgment

Multivariate Gaussian

Opinion dynamics

Pairwise comparison diagram

Pi-lambda theorem

Portmanteau theorem

Preference schedule

Random walk

Range voting

Renewal processes

Riemann-Liouville fractional anti-derivative

Sampling from prescribed distributions

Shannon entropy

Single winner election methods

Smooth, compactly supported functions are dense in L1

Special relativity

Stieltjes length of intervals

Superdiffusion

Tauber's theorem

Uniform convergence of distribution functions

Voting methods

Weibull distributions

Wiener process