(this fundamental result of lebesgue
31Standard probability space — In probability theory, a standard probability space (called also Lebesgue Rokhlin probability space) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940 [1] . He showed that the unit interval endowed with… …
32Euclidean geometry — A Greek mathematician performing a geometric construction with a compass, from The School of Athens by Raphael. Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his… …
33General equilibrium — theory is a branch of theoretical microeconomics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many markets. It is often assumed that agents are price takers and in that setting two common… …
34Convolution — For the usage in formal language theory, see Convolution (computer science). Convolution of two square pulses: the resulting waveform is a triangular pulse. One of the functions (in this case g) is first reflected about τ = 0 and then offset by t …
35Hölder's inequality — In mathematical analysis Hölder s inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of Lp spaces. Let (S, Σ, μ) be a measure space and let 1 ≤ p, q ≤ ∞ with… …
36Convergence of Fourier series — In mathematics, the question of whether the Fourier series of a periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily a given… …
37Cauchy distribution — Not to be confused with Lorenz curve. Cauchy–Lorentz Probability density function The purple curve is the standard Cauchy distribution Cumulative distribution function …
38Characterizations of the exponential function — In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent …
39Grönwall's inequality — In mathematics, Grönwall s lemma allows one to bound a function that is known to satisfy a certain differential or integral inequality by the solution of the corresponding differential or integral equation. There are two forms of the lemma, a… …
40Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …
