In mathematics, a measurable space or Borel space is a basic object in measure theory. It consists of a set and a σ-algebra, which defines the subsets that will be measured. (Wikipedia).
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
Complete metric space: example & proof
This video discusses an example of particular metric space that is complete. The completeness is proved with details provided. Such ideas are seen in branches of analysis.
From playlist Mathematical analysis and applications
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
What is a metric space? An example
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
From playlist Mathematical analysis and applications
Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric
From playlist Topology
MAST30026 Lecture 2: Examples of spaces (Part 1)
I started with the definition of a metric space, we briefly discussed the example of Euclidean space (proofs next time) and then I started to explain a few natural metrics on the circle. Lecture notes: http://therisingsea.org/notes/mast30026/lecture2.pdf The class webpage: http://therisin
From playlist MAST30026 Metric and Hilbert spaces
From playlist Measuring Further Shapes
Is there any place in the Universe where there's truly nothing? Consider the gaps between stars and galaxies? Or the gaps between atoms? What are the properties of nothing?
From playlist Guide to Space
Ohad Kammar: An introduction to statistical modelling semantics with higher-order measure theory
HYBRID EVENT Recorded during the meeting "Logic of Probabilistic Programming" February 04, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiov
From playlist Probability and Statistics
Samplings and Observables. Limits of measured metric spaces - Gabor Elek
Conference on Graphs and Analysis Gabor Elek June 4, 2012 More videos on http://video.ias.edu
From playlist Mathematics
Uri Bader - 1/4 Algebraic Representations of Ergodic Actions
Ergodic Theory is a powerful tool in the study of linear groups. When trying to crystallize its role, emerges the theory of AREAs, that is Algebraic Representations of Ergodic Actions, which provides a categorical framework for various previously studied concepts and methods. Roughly, this
From playlist Uri Bader - Algebraic Representations of Ergodic Actions
Antonio Lerario: Random algebraic geometry - Lecture 1
CONFERENCE Recording during the thematic meeting : "Real Algebraic Geometry" the October 24, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mat
From playlist Algebraic and Complex Geometry
Colloquium MathAlp 2016 - Michel Ledoux
Isopérimétrie dans les espaces métriques mesurés Le problème isopérimétrique (à volume donné, minimiser la mesure de bord, et déterminer les ensembles extrémaux), remonte aux temps les plus anciens. Tout à la fois, il peut se formuler de façon générale dans un espace métrique mesuré, et d
From playlist Colloquiums MathAlp
A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 1
The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who investigated the structure of spaces arising as Gromov-Hausdorff limits of smooth Riemannian manifolds
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 1 (version temporaire)
The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who investigated the structure of spaces arising as Gromov-Hausdorff limits of smooth Riemannian manifolds
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Giovanni Peccati: Some applications of variational techniques in stochastic geometry I
Some variance estimates on the Poisson space, Part I I will introduce some basic tools of stochastic analysis on the Poisson space, and describe how they can be used to develop variational inequalities for assessing the magnitude of variances of geometric quantities. Particular attention
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
The Poisson boundary: a qualitative theory (Lecture 2) by Vadim Kaimanovich
Program Probabilistic Methods in Negative Curvature ORGANIZERS: Riddhipratim Basu, Anish Ghosh and Mahan Mj DATE: 11 March 2019 to 22 March 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore The focal area of the program lies at the juncture of three areas: Probability theory o
From playlist Probabilistic Methods in Negative Curvature - 2019
Covariant Phase Space with Boundaries - Daniel Harlow
More videos on http://video.ias.edu
From playlist Natural Sciences