Problem 1042
If \(\displaystyle \gamma:[0,1]\to \R^2\) is a continuous curve whose image contains \(\displaystyle [0,1]\times [0,1]\) can \(\displaystyle \gamma\) be of bounded variation? Difficulty: 4. |
Problem 1043
Prove that \(\displaystyle f:[0,1]\to \R\) is of bounded variation if and only if it is the sum of two monotonic functions. Difficulty: 6. |
Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government |