4
votes
2answers
99 views

Is the validity of measuring area by approximation an assumption of calculus?

The assumption that if you subdivide an area into more and more sub intervals, the approximation gets better and better. Has this been formally proved, or is it just intuition? Thanks!
0
votes
1answer
118 views

The modulus of curve family

I'm reading book "Geometric function theory and non-linear analysis" and there is one thing that I did not understand. A curve family $\Gamma$ is a collection of curves. An admissible density is ...