Measure theory | Descriptive set theory | Determinacy
In mathematics, a subset of a Polish space is universally measurable if it is measurable with respect to every complete probability measure on that measures all Borel subsets of . In particular, a universally measurable set of reals is necessarily Lebesgue measurable (see below). Every analytic set is universally measurable. It follows from projective determinacy, which in turn follows from sufficient large cardinals, that every projective set is universally measurable. (Wikipedia).
Set Theory (Part 2b): The Bogus Universal Set
Please feel free to leave comments/questions on the video below! In this video, I argue against the existence of the set of all sets and show that this claim is provable in ZFC. This theorem is very much tied to the Russell Paradox, besides being one of the problematic ideas in mathematic
From playlist Set Theory by Mathoma
Every Subset of a Linearly Independent Set is also Linearly Independent Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A proof that every subset of a linearly independent set is also linearly independent.
From playlist Proofs
The perfect number of axioms | Axiomatic Set Theory, Section 1.1
In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T
From playlist Axiomatic Set Theory
What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go
From playlist Set Theory
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
Ex 1: Find Domain and Range of Ordered Pairs, Function or Not
Given a relation as a set of ordered pairs, determine the domain and range. Then determine if the relation is a function. http://mathispower4u.com
From playlist Determining the Domain and Range of a Function
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
The measurement problem and some mild solutions by Dustin Lazarovici (Lecture - 03)
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
Understanding Dark Energy With Most Detailed Supernovae Survey | Dr Dillon Brout
Dark Energy will determine how the Universe will die. With the help of Pantheon+, the most detailed survey of Type 1A supernovae, astronomers can understand more details about Dark Energy and the expansion of spacetime. 👉 Dr Dilon Brout https://pweb.cfa.harvard.edu/people/dillon-brout 🦄
From playlist Interviews
A. Wright - Mirzakhani's work on Earthquakes (Part 1)
We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no familiarity with earthquakes, and the first lecture will be devoted to preliminaries. The s
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Measurement based unitary designs and some applications - D. Markham - Workshop 2 - CEB T2 2018
Damian Markham (LIP6, CNRS, Sorbonne Université) / 05.06.2018 Measurement based unitary designs and some applications Sampling unitaries uniformly from the Haar measure has many applications across quantum information and quantum physics, including benchmarking, private channels, modelli
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
MIT 8.962 General Relativity, Spring 2020 Instructor: Scott Hughes View the complete course: https://ocw.mit.edu/8-962S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx Cosmology continued.  We tie the properties of this spacetime to quantities
From playlist MIT 8.962 General Relativity, Spring 2020
Covariant Observables in Causal Set Quantum Gravityv by Sumati Surya
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
Topologies of nodal sets of random band limited functions - Peter Sarnak
Peter Sarnak Institute for Advanced Study; Faculty, School of Mathematics March 3, 2014 We discuss various Gaussian ensembles for real homogeneous polynomials in several variables and the question of the distribution of the topologies of the connected components of the zero sets of a typic
From playlist Mathematics
WSU: The Accelerating Universe with Adam Riess
Nobel laureate Adam Riess walks you through his team’s incredible discovery of dark energy and our accelerating universe. Explore one of the biggest mysteries in modern cosmology. #WorldSciU This lecture was filmed on May 30, 2015 at the World Science Festival in New York City. Experienc
From playlist WSU Master Classes
Bo'az Klartag - Size of line intersections in high dimensional L_p-balls and product measures
Recorded 07 February 2022. Bo'az Klartag of the Weizmann Institute of Science presents "Size of line intersections in high dimensional L_p-balls and product measures" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Suppose that K is an n-dimensional convex
From playlist Workshop: Calculus of Variations in Probability and Geometry
Listing Subsets Using Tree Diagrams | Set Theory, Subsets, Power Sets
Here is a method for completely listing the subsets of a given set using tree diagrams. It's a handy way to make sure you don't miss any subsets when trying to find them. It's not super efficient, but it is reliable! The process is pretty simple, we begin with the empty set, and then branc
From playlist Set Theory
Determining Cosmological Parameters from CMB & LSS - David Spergel
Prospects in Theoretical Physics Particle Physics at the LHC and Beyond Topic: Determining Cosmological Parameters from CMB & LSS Speaker: David Spergel Date: July 25th, 2017
From playlist PiTP 2017