Measure theory | Articles containing proofs | Inequalities
In mathematical analysis, the Minkowski inequality establishes that the Lp spaces are normed vector spaces. Let S be a measure space, let 1 ≤ p < ∞ and let f and g be elements of Lp(S). Then f + g is in Lp(S), and we have the triangle inequality with equality for 1 < p < ∞ if and only if f and g are positively linearly dependent, i.e., f = λg for some λ ≥ 0 or g = 0. Here, the norm is given by: if p < ∞, or in the case p = ∞ by the essential supremum The Minkowski inequality is the triangle inequality in Lp(S). In fact, it is a special case of the more general fact where it is easy to see that the right-hand side satisfies the triangular inequality. Like Hölder's inequality, the Minkowski inequality can be specialized to sequences and vectors by using the counting measure: for all real (or complex) numbers x1, ..., xn, y1, ..., yn and where n is the cardinality of S (the number of elements in S). The inequality is named after the German mathematician Hermann Minkowski. (Wikipedia).
This is a basic introduction to Minkowski's inequality, which has many applications in mathematics. A simple case in the Euclidean space R^n is discussed with a proof provided.
From playlist Mathematical analysis and applications
A simple proof of a reverse Minkowski inequality - Noah Stephens-Davidowitz
Computer Science/Discrete Mathematics Seminar II Topic: A simple proof of a reverse Minkowski inequality Speaker: Noah Stephens-Davidowitz Affiliation: Visitor, School of Mathematics Date: April 17, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Minkowski Metric | Special Relativity
▶ Topics ◀ Euclidean/Minkowski Metric, Spacelike, Timelike, Lightlike ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on
From playlist Minkowski Diagrams
Minkowski Diagrams | Special Relativity
▶ Topics ◀ Minkowski Diagrams, Event, World Line, Special Relativity ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on P
From playlist Minkowski Diagrams
Solving a linear inequality with fractions
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Summary for solving one variable inequalities
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About
Solving and graphing a linear inequality
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Why do we have to flip the sign when we divide or multiply by negative one - Cool Math
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About
Franz Schuster: Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms
The Blaschke–Santaló inequality is one of the best known and most powerful affine isoperimetric inequalities in convex geometric analysis. In particular, it is significantly stronger than the classical Euclidean Urysohn inequality. In this talk, we present new isoperimetric inequalities fo
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Gaussian Brunn-Minkowski Theory by Mokshay Madiman
PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab
From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY
Minkowski sums, mixed faces and combinatorial isoperimetry - Adiparsito
Computer Science/Discrete Mathematics Seminar II Topic: Minkowski sums, mixed faces and combinatorial isoperimetry Speaker: Karim Adiprasito Date: Tuesday, February 23 I want to sketch some algebraic and geometric tools to solve a variety of extremal problems surrounding Minkowski sums of
From playlist Mathematics
Eugenia Saorin-Gomez - Inner parallel bodies & the Isoperimetric Quotient
Recorded 10 February 2022. Eugenia Saorin-Gomez of the Universität Bremen presents "Inner parallel bodies & the Isoperimetric Quotient" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The so-called Minkowski difference of convex bodies (compact and convex s
From playlist Workshop: Calculus of Variations in Probability and Geometry
Peter Pivovarov: Random s-concave functions and isoperimetry
I will discuss stochastic geometry of s-concave functions. In particular, I will explain how a ”local” stochastic isoperimetry underlies several functional inequalities. A new ingredient is a notion of shadow systems for s-concave functions. Based on joint works with J. Rebollo Bueno.
From playlist Workshop: High dimensional spatial random systems
Mokshay Madiman : Minicourse on information-theoretic geometry of metric measure
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Geometry
Emanuel Milman - The log-Minkowski Problem - IPAM at UCLA
Recorded 09 February 2022. Emanuel Milman of Technion - Israel Institute of Technology presents "The log-Minkowski Problem" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The classical Minkowski problem asks to find a convex body K in Rn having a prescrib
From playlist Workshop: Calculus of Variations in Probability and Geometry
Ramon van Handel: The mysterious extremals of the Alexandrov-Fenchel inequality
The Alexandrov-Fenchel inequality is a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes. It is one of the central results in convex geometry, and has deep connections with other areas of mathematics. The characterization of its extremal bodie
From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability
Functional Analysis - Part 20 - Minkowski inequality
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Functional analysis series: https://www.youtube.com/playlist?list=PLBh2i93oe2qsGKDOsuVVw-OCAfprrnGfr PDF versions: https://steadyhq.com/en/brightsideofmaths/po
From playlist Functional analysis
Yashar Memarian: A Brunn Minkowski type inequality on the sphere
The lecture was held within the framework of the Hausdorff Trimester Program: Optimal Transportation and the Workshop: Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis
From playlist HIM Lectures 2015
How to solve and graph one variable inequalities
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About