Concept

Bounded function

Related lectures (32)

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Derivable Functions: Limits and Continuity

Explores derivable functions, limits, continuity, and differentiability, emphasizing the relationship between them.

Interior Points and Compact Sets

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Analysis I: Decreasing and Growing Functions

Explores decreasing and growing functions, bounded sequences, and limit existence.

Convergence and Limits in Real Numbers

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Sequences and Convergence: Solutions to Exercises

Covers solutions to exercises related to sequences, convergence, bounded functions, and bijective functions.

Subsequences and Bolzano-Weierstrass Theorem

Covers the proof of the Squeeze Theorem, Quotient Criteria, and the Bolzano-Weierstrass Theorem.

Convergence Criteria

Covers the convergence criteria for sequences, focusing on the definition of convergence and the properties of convergent sequences.

Limits of Sequences

Covers the concept of limits of sequences, including definitions, examples, boundedness, and more.

Functional Calculus: Simple Functions

Covers the extension of functional calculus to simple functions and the concept of *-homomorphism.

Generalized Integrals: Definition and Convergence

Covers the definition and convergence of generalized integrals over bounded and unbounded intervals.

Unbounded Positive Sequences

Explores finding positive unbounded sequences and their properties, including limits at infinity.

Functional Analysis I: Operator Definitions

Introduces linear and bounded operators, compact operators, and the Banach space.

Convergent Sequences: Definitions and Illustrations

Explains convergent sequences, bounded sequences, subsequences, and compact sets with illustrations and proofs.

Convergence of Sequences: Examples and Theorems

Explores the convergence of sequences through examples and theorems.

Compact Sets and Extreme Values

Explores compact sets, extreme values, and function theorems on bounded sets.

Mild Dissipative Surface Dynamics

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Uniform Integrability and Convergence

Explores uniform integrability, convergence theorems, and the importance of bounded sequences in understanding the convergence of random variables.