Prove the excision property for the outer measure m∗ , that is “If A is a measurable set and B ⊇ A, then prove m∗ (B \ A) = m∗ (B) − m∗ (A).” (Note that B \ A is the set minus {x ∈ B : x /∈ A}.are you can solve it
Watched the introduction video and halfway to this one. I'm a bit interested in probability so this series seemed like something that would interest me. Still liking your explanations! One thing I've noticed: You use the ping cursor a lot, I wonder if it is always needed. I'm watching on a big screen so I don't really need it almost at all. Maybe you can try various ways but maybe when you are reading a definition it would suffice that you ping at the first word and then glide he cursor across the words as you read them instead of pinging every word?
What courses are prerequisite for the most intuitive understanding of this material? It's nice, it gives some nuance to some discrete probability outcomes- but definitely a bit more rigorous than the undergraduate perspective. I want to see if I can do independent study measure theory before I graduate though. Any suggestions?
Help me, please. A_1, . . . , A_k are disjoint sets in B[0, ∞) × B (R\{0}), where B is a Borel set and x is the cartesian product. How do we interpret B[0, ∞) × B (R\{0})?
There is no way is F3 is a sigma- algebra. That is misleading for the people watching! When omega has more than two elements then F3 is not closed under countable unions
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Prove the excision property for the outer measure m∗
, that is
“If A is a measurable set and B ⊇ A, then prove
m∗
(B \ A) = m∗
(B) − m∗
(A).”
(Note that B \ A is the set minus {x ∈ B : x /∈ A}.are you can solve it
Hi, can you show me how to prove the σ-alg. over countable sets at 11:30 ? Thank you
Watched the introduction video and halfway to this one. I'm a bit interested in probability so this series seemed like something that would interest me. Still liking your explanations! One thing I've noticed: You use the ping cursor a lot, I wonder if it is always needed. I'm watching on a big screen so I don't really need it almost at all. Maybe you can try various ways but maybe when you are reading a definition it would suffice that you ping at the first word and then glide he cursor across the words as you read them instead of pinging every word?
Thank you for your feedback! Maybe I will try to use the ping cursor a little less (especially if there is a lot of text on the screen).
附
What courses are prerequisite for the most intuitive understanding of this material? It's nice, it gives some nuance to some discrete probability outcomes- but definitely a bit more rigorous than the undergraduate perspective. I want to see if I can do independent study measure theory before I graduate though. Any suggestions?
analysis 3 i suppose
角日
Very clear, thank you!
Help me, please.
A_1, . . . , A_k are disjoint sets in B[0, ∞) × B (R\{0}), where B is a Borel set and x is the cartesian product.
How do we interpret B[0, ∞) × B (R\{0})?
very good
Hi, can you give an real-life example of Borel sigma?
That cursor effect is distracting. Reading slides does not make a good lecture. Slides should augment your words, not mirror them.
束中一
k
That means a empty set is always a generated sigma algebra. Am I correct?
Is the complement of the empty set also in the set?
@@thangible this set is closed and open in the topological sense
@@thangible o: of course, the compliment of phi is the set omega which is contained in F but F in turn is contained in the power set of omega.
There is no way is F3 is a sigma- algebra. That is misleading for the people watching! When omega has more than two elements then F3 is not closed under countable unions