How deep Sets affect Measure Theory?

[zli034]

Guys,

I'm taking real analysis starting with open, close, compact sets, and neighborhoods. Now I'm addict to rely on these concepts to do my proofs. In the future I will have to take Measure Theory. Can anyone give me a percentage indication for how many percent theorems are proven by the set concepts?

I'm really happy with sets.

zli034

 

[Eynstone]

Measure theory is really set theory at its core.

 

[micromass]

Guys,

I'm taking real analysis starting with open, close, compact sets, and neighborhoods. Now I'm addict to rely on these concepts to do my proofs. In the future I will have to take Measure Theory. Can anyone give me a percentage indication for how many percent theorems are proven by the set concepts?

I'm really happy with sets.

zli034

If you mean how often are sets used in measure theory: 100%
If you mean how often are topological arguments (such as closed, open, compact) used: it depends, but perhaps 50%