Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2008-07-30 12:48:15

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

σ-algebra

smile

Offline

#2 2008-07-30 23:10:20

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: σ-algebra

smile

Offline

#3 2008-09-26 06:39:11

TooT
Member
Registered: 2008-09-20
Posts: 4

Re: σ-algebra


TooT.

Offline

#4 2008-09-26 06:50:57

TooT
Member
Registered: 2008-09-20
Posts: 4

Re: σ-algebra


TooT.

Offline

#5 2008-09-27 11:42:00

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: σ-algebra

The concept of a sigma algebra is particularly useful in analysis.  It can actually be quite difficult to prove that any explicit set is (Lebesgue) measurable.  However, the set of measurable sets forms a sigma algebra.  Using this fact, we can get a whole lot of sets by simply proving that all open and closed sets are measurable.  In particular, given those facts any Borel set is indeed measurable.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

#6 2008-09-30 09:29:06

TooT
Member
Registered: 2008-09-20
Posts: 4

Re: σ-algebra

And indeed, sigma-algebras are a kind of introduction to measure theory (Borel and Lebesgue measures in particular)

Last edited by TooT (2008-09-30 09:29:26)


TooT.

Offline

Board footer

Powered by FluxBB