/sci/ - Science & Math » Thread #11197360

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Anonymous Wed 04 Dec 02:24:19 2019 No.11197360 View Reply Original Report

Quoted By: >>11197478 >>11198034

i dont understand Borel sets intuitively

can you help me out?

Anonymous

Anonymous Wed 04 Dec 2019 02:29:44 No.11197373 Report

Quoted By:

"nice sets"

there you go

Anonymous

Anonymous Wed 04 Dec 2019 03:09:54 No.11197478 Report

Quoted By: >>11197541 >>11197710

>>11197360
The smallest sigma algebra generated by the open sets of the topology?

There isnt a deep idea going on. measure theory is just technical work to make sure integrals don't have pathological behavior.

Anonymous

Anonymous Wed 04 Dec 2019 03:32:51 No.11197541 Report

Quoted By:

>>11197478

do you mean "paradox" integrals?

Anonymous

Anonymous Wed 04 Dec 2019 04:49:57 No.11197710 Report

Quoted By: >>11197846 >>11198028

>>11197478
You don't need a topology to define a measurable space.

Anonymous

Anonymous Wed 04 Dec 2019 05:35:07 No.11197846 Report

Quoted By:

>>11197710
??? Nobody argued that?
We want to link the topological structure of the space with measure. Just taking sets in the topology is too coarse, Borel sets are just the thing that covers reasonable useful sets.

Anonymous

Anonymous Wed 04 Dec 2019 07:48:50 No.11198028 Report

Quoted By:

>>11197710
brainlet detected

Anonymous

Anonymous Wed 04 Dec 2019 07:53:49 No.11198034 Report

Quoted By:

>>11197360
The basic definition $F, F\sigma, F\sigma\delta,\ldots$ helps you understand ordinal numbers better so it's worth learning. There is also an alternative definition using what are called "analytic sets" in set theory: X is borel iff X and its complement are both analytic in this sense.

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