Cantor Sets
Not what you're looking for?
1. Show that the Cantor function c: [0, 1] → [0, 1] is continuous.
To do this, I know I need to use the fact that c is monotone, but I'm having difficulty from there.
2. Compute ∫c, where c is considered to be an element of L+(R). (let c(x) =0 for x not in [0, 1])
Here, c is the Cantor Function and L+(R) consists of functions which are almost everywhere the limit of a non-decreasing sequence of step functions for which the sequence (∫cn) is bounded.
3. Show that ¼ is in the Cantor set.
See attached file for full problem description.
Purchase this Solution
Solution Summary
Cantor sets are investigated. The solution is detailed and well presented.
Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Probability Quiz
Some questions on probability