Definitions of mathematical integration | Functional analysis | Expected utility

Choquet integral

A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical mechanics and potential theory, but found its way into decision theory in the 1980s, where it is used as a way of measuring the expected utility of an uncertain event. It is applied specifically to membership functions and capacities. In imprecise probability theory, the Choquet integral is also used to calculate the lower expectation induced by a 2-monotone lower probability, or the upper expectation induced by a 2-alternating upper probability. Using the Choquet integral to denote the expected utility of belief functions measured with capacities is a way to reconcile the Ellsberg paradox and the Allais paradox. (Wikipedia).

Video thumbnail

What is an integral and it's parts

👉 Learn about integration. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which the upper and the lower li

From playlist The Integral

Video thumbnail

Integrate cosine using u substitution

👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t

From playlist The Integral

Video thumbnail

Sergiu Klainerman - Are Black Holes Real

Sergiu Klainerman (Princeton University) - Are Black Holes Real

From playlist Conférence en l'honneur d'Yvonne Choquet-Bruhat

Video thumbnail

Piotr Chrusciel - The Many Ways of the Characteristic Cauchy Problem

Piotr Chrusciel (University of Vienna) - The Many Ways of the Characteristic Cauchy Problem

From playlist Conférence en l'honneur d'Yvonne Choquet-Bruhat

Video thumbnail

Tommaso Ruggeri - Recent Mathematical Results in Classical and Relativistic Extended Thermodynamics

Tommaso Ruggeri (University of Bologna) ­- Recent Mathematical Results in Classical and Relativistic Extended Thermodynamics

From playlist Conférence en l'honneur d'Yvonne Choquet-Bruhat

Video thumbnail

Vincent Moncrief - Reflections on U(1) Invariant Einsteinian Universes

Vincent Moncrief (Dpt of Physics and Mathematics, Yale University) ­ - Reflections on U(1) Invariant Einsteinian Universes

From playlist Conférence en l'honneur d'Yvonne Choquet-Bruhat

Video thumbnail

S. Druel - A decomposition theorem for singular spaces with trivial canonical class (Part 5)

The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, an irreducible, simply-connected Calabi-Yau, and holomorphic symplectic manifolds. With the deve

From playlist Ecole d'été 2019 - Foliations and algebraic geometry

Video thumbnail

U substitution with trig sine and cosine

👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t

From playlist The Integral

Video thumbnail

How to u substitution to natural logarithms

👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t

From playlist The Integral

Video thumbnail

Helmut Friedrich - On Anti-de Sitter Type Space-Times

Helmut Friedrich (Max-Plank-Institut fuer Gravitationsphysik, Potsdam) - On Anti-de Sitter Type Space-Times

From playlist Conférence en l'honneur d'Yvonne Choquet-Bruhat

Video thumbnail

Apply u substitution to a polynomial

👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t

From playlist The Integral

Video thumbnail

A Trig Integral to Complement your Day

We have a trig integral with sines and cosines everywhere, but we can't figure out the antiderivative! Luckily, it's a definite integral, so we don't have to.

From playlist Integrals

Video thumbnail

Antoine Triller - Communication entre neurones : instabilité moléculaire et mémoire

Communication entre neurones : instabilité moléculaire et mémoire, du normal au pathologique Les neurones communiquant entre eux forment des réseaux qui sont à l’origine des propriétés du système nerveux. Les neurones communiquent entre eux au niveau de jonctions appelées « synapses ». Le

From playlist Évenements grand public

Video thumbnail

Jim Isenberg - The Conformal Method and Solutions of the Einstein Constraint Equation

Jim Isenberg (University of Oregon) - The Conformal Method and Solutions of the Einstein Constraint Equation : Success, and Looming Difficulties

From playlist Conférence en l'honneur d'Yvonne Choquet-Bruhat

Video thumbnail

How to use u substitution to find the indifinite integral

👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t

From playlist The Integral

Video thumbnail

Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard

PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis

From playlist Ergodic Theory and Dynamical Systems 2022

Video thumbnail

Integral e to arccos

Integral of e to the arccos In this crazy video, I evaluate the integral of e to the arccos, using a clever trick, with a sprinkle of integration by parts. Enjoy! Note: Thank you Nathan for this idea! Check out my Integrals playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmDfG

From playlist Integrals

Video thumbnail

Learn how to use u substitution to integrate a polynomial

👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t

From playlist The Integral

Video thumbnail

Alain Connes: Towards a Weil cohomology

The lecture was held within the framework of the Hausdorff Trimester Program: Non-commutative Geometry and its Applications and the Workshop: Number theory and non-commutative geometry 26.11.2014

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

Video thumbnail

Apply u substitution with a binomial squared

👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t

From playlist The Integral

Related pages

Set function | Nonlinear expectation | Superadditivity | Subadditivity | Capacity of a set | Allais paradox | Decision theory | Upper and lower probabilities | Imprecise probability | Cumulative distribution function | Membership function (mathematics) | Riemann integral | Ellsberg paradox | Potential theory