Lectures related to Locally integrable function

Existence of Solutions for Poisson-Dirichlet Problem

Covers the existence of solutions for the Poisson-Dirichlet problem, focusing on showing that certain conditions hold for locally bounded and Hölder continuous functions.

Analysis IV: Convergence Theorems and Integrable Functions

Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.

Kirillov Paradigm for Heisenberg Group

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Analysis II: Abstract Integration

Explores abstract integration of functions and the need for stronger conditions beyond continuity.

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Differential Forms and Invariant Measures

Covers differential forms, invariant measures, and integration on manifolds with examples and illustrations.

Calculus of Variations: Radon-Nikodym Theorem

Covers the Radon-Nikodym theorem and the uniqueness of signed Borel measures.

Integral Calculation of Functions

Explains firm pavements, Darboux sums, and the conditions for a function to be integrable.

Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Multiple Integrals: Definition and Properties

Covers the definition of multiple integrals, volume calculation, tensorial partitions, and integrable functions.

Graph Surfaces: Integration and Vector Calculus

Covers integrating functions over graph surfaces in vector calculus, emphasizing the interpretation of divergence theorem and special cases of domain between two graphs.

Multiple integrals: definition, properties, and applications

Covers the definition and properties of multiple integrals, including partitions and the theorem of Fubini.

Integration: Taylor Approximation & Convex Functions

Covers Taylor approximation, convex functions, and integrable properties.

Pointed Mapping Spaces: Exponential Law and Adjunction

Explores pointed mapping spaces, the exponential law, adjunction properties, and homotopic classes.

Riemann Integral: Properties and Generalization

Explores characterizations and generalizations of the Riemann integral, showcasing its properties and applications.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Riemann Integral: Techniques and Fundamentals

Explores Riemann integrability, the fundamental theorem of integral calculus, and various integration techniques.

Compact-open topology

Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.

Expectation of a Random Variable

Defines the expectation for random variables, emphasizing the importance of absolute values.

Exponential Law: Mapping Spaces and Compactness

Explores the exponential law for mapping spaces and the role of compactness in topological theory.