Probabilistic inequalities

a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas. It is considered to be one of the most important inequalities in all of mathematics

theorem of convex functions

inequality applying to random variables with finite expected values

inequality applying to non-negative random variables

inequality between integrals in Lp spaces

theorem that gives bounds on integrals of functions

exponentially decreasing bounds on tail distributions of sums of independent random variables

inequality applying to probability spaces

probabilistic inequality of partial sums of independent random variables

probabilistic inequality applying on sum of bounded random variables

theorem

theorem describing the rate at which the probability distribution of the scaled mean of a random sample converges to a normal distribution as the sample size increases

probabilistic inequality

inequality applying to (sub-)martingales

probability theorem

probabilistic inequality relating to concentration of random variables

probabilistic inequality applying to martingales with bounded differences

inequality for real numbers

probabilistic inequality on unimodal random variable

inequality applying to finite variance random variables

mathematical construction of a martingale (with respect to a given filtration) approximating a given random variable; the evolving sequence of best approximations to the random variable based on information accumulated up to a certain time