Abhijeet Mulgund's Personal Webpage

TODO

Last updated Nov 1, 2022

Graph exclude

Backlinks

Home Page
A Closed Convex Set is the Intersection of all Closed Halfspaces containing it
A Connected Set is Pathwise Connected in a Metric Space
A Hilbert Space has a Countable Orthonormal Basis iff it is Separable
A Linear Equation System is Homogenous iff its constants are 0
A Nonempty Set is Compact in the Order Topology iff it is Tightly Bounded and Complete
A Normed Vector Space is Complete iff all Absolutely Convergent Series Converge
A Normed Vector Space is a Topological Vector Space
A Real Vector Space over the Rational Field is Infinite-Dimensional
A Sequence Converges on the Extended Reals iff the number of Complete Upcrossings is Finite
A Sequence of Gaussian Random Variables that converge in L1 converge to a Gaussian
A Sequence of L1 Random Variables is L1 convergent iff they converge in probability and are Uniformly Integrable
A Set is Closed in a First Countable Space iff it contains all its Sequential Limits
A Vector Space is Infinite-Dimensional iff its Linearly Independent Set Size is Unbounded
A finite measure is absolutely continuous wrt another iff small sets on the other measure are also small on it
A sigma-finite measure is absolutely continuous wrt another sigma-finite measure iff their Radon-Nikodym Derivative exists
About Me
Absolute Continuity
All Simple Functions can be Written in Standard Form
Alternate Option for CE
Augmenting Path Theorem of Matchings
Banach Spaces are Separable if they contain a Countable Total Subset
Basic Properties of Bi-Ordered Groups
Borel-Cantelli Lemma
Cardinal Arithmetic
Characteristic Function
Characterization of Convex Polytope Faces
Characterization of Minimal Faces
Closed Halfspace
Closed Subset of a Complete Space is Complete
Closure
Coincidence Lemma
Compact Sets are Bounded
Completeness of the Real Numbers
Complex Numbers
Components Converge iff Sequence Converges in Finite Product Metric Spaces
Conditional Expectation
Conditional Expectation Algorithm for Max-Cut approximation
Conditional Expectation is Linear
Conditional Expectation with respect to Sigma Field
Conditional Probability
Construction of Brownian Motion
Continuity Theorem
Continuous Function
Continuous Functions on a Compact Set are Banach
Continuous Mapping Theorem
Convergence in L1 implies convergence of Integrals
Convex Polytope Face
Convex Sets contain their Expectation
Correspondence of Lebesgue-Stieltjes Measures and Distribution Functions
Correspondence of Surjective Functions, Partitions, and Equivalence Relations
Countable Set Sigma Algebra
Countable Set Sigma Algebra is Generated by Singletons
Dense
Direct Product Vector Space
Disjoint Compact Sets are Separable from each other in a Hausdorff Space
Disjoint Sets
Dot Product of Random Vector and Independent Entry Random Vector
Elementary Row Operation
Equivalent Conditions for Convexity
Equivalent Conditions for being a Sigma Field up to a Stopping Time
Euler's Formula
Every Countable Total Ordering Order Embeds into the Rationals
Every Net on a Total Ordering has a Monotone Subnet
Every Vector Space has a Basis
Existence of Moment Generating Functions imply Existence of Moments
Extended Real Numbers
Finite Dimension of a Proper Subspace is less than Dimension of Parent Vector Space
Finite Intersections of Open Balls contain Open Balls about each point
Finite Normed Vectors form a Normed Vector Space
Fourier Expansion of a Pseudo-Boolean Function
Frechet Derivative
Frobenius Inner Product
Function Composition
Gaussian Elimination
Gaussian Random Variable
Graph Connected Component
Graph Edge
Guassian Random Variables are independent iff their Covariance is 0
Halfspaces are Convex Sets
Heine Criterion
House Rules and Conventions
Hyperplane
Hyperplanes are Affine Sets
If Space is a Standard Probability Space, then a Regular Conditional Distribution exists and is Almost Surely Unique
If small sets on one measure are also small on another measure then it is absolutely continuous wrt the other
Independence
Inner Product
Inner Products are Linear in their first argument
Integration
Integration of a Nonnegative Function is 0 iff the Function is 0 Almost Everywhere
Interior of Convex Set is Convex
Inverse Reinforcement Learning
Inverting Right Continuous Inverses does not decrease
Kolmogorov Strong Law of Large Numbers
Kolmogorov Three Series Theorem
Konig's Theorem
L1 is a Complete Metric Space
Levy's Theorem
Liminf of Indicator Sequence is Indicator of Liminf
Linear Matrix Inequality
Linear Operator
Linear Operators preserve 0
Linear Program
Lp Space
Manifolds have a Countable Basis of Precompact Coordinate Balls
Markov Process
Matching
Matrix Equation Systems are Linear Systems
Matrix Multiplication is a Linear Function
Matrix Representation of Elementary Row Operations
Measureable Set
Natural Numbers are Well-Ordered
Nondeterministic Polynomial Time Solvable
Nonempty Compact Sets are Tightly Bounded
Open Halfspace
Optimal Solution Set of Linear Program is a Face of Constraint Polytope
Optimal Solution of Bounded Linear Program is at Vertex
Order Topology coincides with Metric Topology on the Real Numbers
Path-Connected implies Connected
Product Topological Space
Product of Finitely Many Proper Open Sets form a Basis for the Product Topology
Quotient Norm
Quotient Normed Space of a Banach Space is Banach
Quotient Vector Space
RNA World Hypothesis
Rationals are Dense in the Reals
Research
Right Continuous Inverse
Row Equivalent Matrix Systems have the same Solution Set
Scheffe's Lemma
Semidefinite Program
Sentence Satisfaction under one Assignment means Satisfaction under all Assignments
Sequence Convergence
Set Intersection
Sigma-Finite Measure
Solution set of Linear Equations is an Affine Set
Standard Borel Space
Standard Probability Space
Stock
Stopping Time
Strictly Convex Function
Support of a Measureable Function
Support of a Random Element
Supremum of Negative is Negative of Infimum
Taylor's Theorem
The Closed Unit Ball of a Normed Vector Space is Compact iff the Dimension is Finite
The Formula Set is the Union of Formula Sets of all Complexities
The Lp Space of a Separable Measure Space is Separable
The Order Topology on a Subset is the Subset Topology
The Restriction of Homeomorphism is a Homeomorphism in the Subspace Topology
Topological Invariance of Dimension
TurboAE
Tutte-Berge Formula
Tutte's Matching Theorem
Uniform Integrability
Univariate Polynomials on Complex Numbers are Infinite-Dimensional
Univariate Polynomials on Real Numbers are Infinite-Dimensional
Vertex Cover and Matching Duality
c0 is Banach
little-lp Space

TODO

Backlinks

Interactive Graph