Uniform Convergence - 24
An important question is which function properties are preserved by the pointwise limit. If all of the functions in the sequence are continuous, must the limit be continuous? Are derivatives preserved? What about integrals? Perhaps we will need a stronger notion of convergence if we hope to preserve nice function properties.
Reading: Familiarize yourself with the definition of Uniform Convergence (Rudin p. 147, Definition 7.7).
Pre-Lecture Materials
In-Class Activities
Open the following Overleaf link and make a copy for yourself. Remember to include the names of everyone who worked together in the document.
Lecture 24 In-Class Activity: Weierstrass and Uniform Convergence
Assignments
- Submit Overleaf Proof 24: Uniform Convergence