Uniform convergence
Not what you're looking for?
Note: all of the following _n denote n as a subscript.
Suppose {f_n} from n = 0 to infinity, is a sequence of functions converging uniformly to a function f on an interval [a,b]. Also assume that the sequence has a uniform bound i.e. there exists M1 such that for all positive integers n, | f_n(x) | < = M1 for all x belonging to [a,b], and that there exists M2 such that | f(x) | < = M2 for all x belonging to [a,b], i.e. f is also bounded. Show that the sequence f_n^2 converges uniformly to f^2.
Purchase this Solution
Solution Summary
This solution helps explore uniform convergence within the context of functions & calculus
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.