Measure theory | Descriptive set theory
In measure theory, projection maps often appear when working with product spaces: The product sigma-algebra of measurable spaces is defined to be the finest such that the projection mappings will be measurable. Sometimes for some reasons product spaces are equipped with sigma-algebra different than the product sigma-algebra. In these cases the projections need not be measurable at all. The projected set of a measurable set is called analytic set and need not be a measurable set. However, in some cases, either relatively to the product sigma-algebra or relatively to some other sigma-algebra, projected set of measurable set is indeed measurable. Henri Lebesgue himself, one of the founders of measure theory, was mistaken about that fact. In a paper from 1905 he wrote that the projection of Borel set in the plane onto the real line is again a Borel set. The mathematician Mikhail Yakovlevich Suslin found that error about ten years later, and his following research has led to descriptive set theory. The fundamental mistake of Lebesgue was to think that projection commutes with decreasing intersection, while there are simple counterexamples to that. (Wikipedia).
Linear functions -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
Multivariable Calculus | The projection of a vector.
We define the projection of a vector in a certain direction. As an application we decompose a vector into the sum of a parallel and orthogonal component. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
Vector Projection Explained Geometrically
A purely geometric derivation of the dot product
From playlist Summer of Math Exposition 2 videos
What is the projection of one vector on another one and how is it useful? Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/CpZUX1mFLS
From playlist Introduction to Vectors
We introduce the idea of dimensional analysis and its use in finding unknown quantities' dependence on relevant dimensionful variables.
From playlist Mathematical Physics I Uploads
In this second part on Motion, we take a look at calculating the velocity and position vectors when given the acceleration vector and initial values for velocity and position. It involves as you might imagine some integration. Just remember that when calculating the indefinite integral o
From playlist Life Science Math: Vectors
Proving that orthogonal projections are a form of minimization
Description: Orthogonal projections provide the closest point on a subspace to some point off the subspace. We use Pythagoras to prove that this is always the case. Learning Objective: 1) Given a subspace and a point, compute the closest point in the subspace to the given point. This
From playlist Linear Algebra (Full Course)
An introduction to the idea of Dimensional Analysis
From playlist Mathematical Physics I Uploads
A mathematics bonus. In this lecture I remind you of a way to calculate the cross product of two vector using the determinant of a matrix along the first row of unit vectors.
From playlist Physics ONE
Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w
From playlist Mathematics
Stanford Seminar - Towards theories of single-trial high dimensional neural data analysis
EE380: Computer Systems Colloquium Seminar Towards theories of single-trial high dimensional neural data analysis Speaker: Surya Ganguli, Stanford, Applied Physics Neuroscience has entered a golden age in which experimental technologies now allow us to record thousands of neurons, over
From playlist Stanford EE380-Colloquium on Computer Systems - Seminar Series
Colloquium MathAlp 2016 - Vincent Vargas
La théorie conforme des champs de Liouville en dimension 2 La théorie conforme des champs de Liouville fut introduite en 1981 par le physicien Polyakov dans le cadre de sa théorie des sommations sur les surfaces de Riemann. Bien que la théorie de Liouville est très étudiée dans le context
From playlist Colloquiums MathAlp
Measurements vs. Bits: Compressed Sensors and Info Theory
October 18, 2006 lecture by Dror Baron for the Stanford University Computer Systems Colloquium (EE 380). Dror Baron discusses the numerous rich insights information theory has to offer Compressed Sensing (CS), an emerging field based on the revelation that optimization routines can reco
From playlist Course | Computer Systems Laboratory Colloquium (2006-2007)
A Theory of Neural Dimensionality, Dynamics and Measurement by Surya Ganguli
ICTS at Ten ORGANIZERS: Rajesh Gopakumar and Spenta R. Wadia DATE: 04 January 2018 to 06 January 2018 VENUE: International Centre for Theoretical Sciences, Bengaluru This is the tenth year of ICTS-TIFR since it came into existence on 2nd August 2007. ICTS has now grown to have more tha
From playlist ICTS at Ten
Weak measurements by Alex Matzkin (Lecture - 01)
21 November 2016 to 10 December 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Quantum Theory has passed all experimental tests, with impressive accuracy. It applies to light and matter from the smallest scales so far explored, up to the mesoscopic scale. It is also a necessary ingredie
From playlist Fundamental Problems of Quantum Physics
A new basis theorem for ∑13 sets
Distinguished Visitor Lecture Series A new basis theorem for ∑13 sets W. Hugh Woodin Harvard University, USA and University of California, Berkeley, USA
From playlist Distinguished Visitors Lecture Series
THE BASICS:: Rudiments of Linear Perspective 1-Pt. #1
Introduction to Linear Perspective, Space creation, depth, illusion of 3-D reality on 2-D surface. The Perspective videos in the Basics Section are meant to be introductory and about process and visualization and are not completely accurate but are aesthetically conclusive. For the most ac
From playlist THE BASICS
Stability of the set of quantum states - S. Weis - Workshop 2 - CEB T3 2017
Stephan Weis / 26.10.17 Stability of the set of quantum states A convex set C is stable if the midpoint map (x,y) - (x+y)/2 is open. For compact C the Vesterstrøm–O’Brien theorem asserts that C is stable if and only if the barycentric map from the set of all Borel probability measures to
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester