Complex 'Measure Theory'

[Terry Giblin]

Can anyone please recommend, any good online lectures, on the following subjects?

Measure Theory (http://mathworld.wolfram.com/MeasureTheory.html)

Complex Measure Theory (http://mathworld.wolfram.com/ComplexMeasure.html)

Light in, Light out.

Thank You.

[peter eldergill]

When I took Measure Theory, "online lectures" didn't really exist..sorry..I can't help. (BTW that was in about 1997, so the intertoobs existed, but not for lectures yet, at least not that I knew of back then)

Pete

[Ivan Viehoff]

In terms of measure theory, what are you wanting this for? Are you seeing it as part of functional analysis, or are you seeing it as the foundation of probability theory? Where you are expecting to take it probably depends what sort of approach you want. Here's a very basic introduction https://www.ee.washington.edu/techsite/papers/documents/UWEETR-2006-0008.pdf with a further reading list.

Complex measure is pretty abstruse. I doubt you'll find anything like a course on it. More like a 10 minute aside in a functional analysis course.

[Terry Giblin]

A few weeks ago, I watched the lecture by Peter Orbanz, in which he mentions Measure Theory.

http://videolectures.net/mlss09uk_orbanz_fnbm/

I then read a book called complex variables and applications, by Brown & Churchill.

Now I am reading The Art of Probability: For Scientists and Engineers.

http://ecx.images-amazon.com/images/I/41Iv0qnueqL.jpg

Question: How many ways can I calculate P(B¦A)?

Light in, Light out.

[tashirosgt]

A few weeks ago, I watched the lecture by Peter Orbanz, in which he mentions Measure Theory.

http://videolectures.net/mlss09uk_orbanz_fnbm/

I then read a book called complex variables and applications, by Brown & Churchill.

Now I am reading The Art of Probability: For Scientists and Engineers.

http://ecx.images-amazon.com/images/I/41Iv0qnueqL.jpg



That's doesn't clarify your quest except to those who want to repeat that experience from your sources!



Question: How many ways can I calculate P(B¦A)?



Perhaps if you gave examples of what you consider different ways to calculate P(B|A), your question would be clear.

[Terry Giblin]

Dear tashirosgt,

Have you studied Measure Theory?


That's doesn't clarify your quest except to those who want to repeat that experience from your sources!

I thought it was polite to quote your references.

Can you recommend any books, lectures or webcasts?

Talking of which, I to would like to recommend A Measure Theory Tutorial (Measure Theory for Dummies) (https://www.ee.washington.edu/techsite/papers/documents/UWEETR-2006-0008.pdf) by Prof Gupta.


Perhaps if you gave examples of what you consider different ways to calculate P(B|A), your question would be clear.

Once you ask the right question, the rest of the answers are easy.

Can you pick any branch of mathematics or physics, which is not derived from 'measure theory'? - By definition.

Light in, Light out.

[Terry Giblin]

Complex measure is pretty abstruse.

To explain or understand?


I doubt you'll find anything like a course on it. More like a 10 minute aside in a functional analysis course.

We all have to agree on at least one thing, anything, something.

I am simply asking to start a discussion on Measure Theory.

Complex 'Measure Theory' for Dummies.

Light in, Light out.

[tashirosgt]

Dear tashirosgt,

Have you studied Measure Theory?



Yes.




I thought it was polite to quote your references.



I agree that it's useful to provide references and specific examples to supplement a question, but it is polite to ask the question so it can be understood without consulting the references.



Can you recommend any books, lectures or webcasts?


The text I had was "Measure, Integration And Functional Analysis" by Ash. It was OK for me. I was math major.




Once you ask the right question, the rest of the answers are easy.



You haven't explained your question about P(A|B) yet.




Can you pick any branch of mathematics or physics, which is not derived from 'measure theory'? - By definition.



Yes. Why would you think that all branches of mathematics are derived from measure theory?

[pzkpfw]

Can anyone please recommend, any good online lectures, on the following subjects?...


... I am simply asking to start a discussion on Measure Theory. ...


Which is it, Terry Giblin?

You are acting all mysterious again, and will soon be infracted once more.

[Ivan Viehoff]

Complex measure is pretty abstruse.
To explain or understand?
Sorry, a poor choice of word. I meant that it is rare, obscure, and little studied, because we we haven't found much use for it. In many ways, the whole point of measures, in general, is that they are real, not complex. When they stop being real, most of what you know about them goes out of the window. For example a basic property of real measures is that they are monotonic. Probability, for example, makes little sense as a complex number. One application it can have is in the study of the Riesz Representation Theorems, the complex version (see wiki article thereon), so I did wonder if you were interested in that, but I decided not to put the words into your mouth.

I am simply asking to start a discussion on Measure Theory.
Complex 'Measure Theory' for Dummies.
In general, in mathematics, the complex version of something is not just a simple extension of the real version of something. Complex analysis has a whole completely different flavour and application from real analysis. So which do you want, (real) Measure theory, the much studied (well, moderately popular) useful subject, or complex measure theory, the very rare, really rather different, and not very useful thing? Make your mind up.

[Terry Giblin]

Dear Ivan,

You definitely know your subject, can we please talk?

I have lots of questions, I would like to ask you.

Do you use Skype? - 'Terry Giblin Jarrow'

Light in, Light out.

[Terry Giblin]

For completeness I just found another good book called, An introduction to Measure theory (http://terrytao.files.wordpress.com/2011/01/measure-book1.pdf) - By Terence Tao

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[Terry Giblin]

To understand 'Measure theory' fully, you have to understand Open and Closed Sets (http://en.wikipedia.org/wiki/Open_set)...

http://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Red_blue_circle.svg/200px-Red_blue_circle.svg.png

Example: The points (x, y) satisfying x2 + y2 = r2 are colored blue. The points (x, y) satisfying x2 + y2 < r2 are colored red. The red points form an open set. The union of the red and blue points is a closed set.

Do you remember ' http://www.gogeometry.com/e_i_pi_full.jpg '

Starting to get the picture?

Light in, Light out.

[HenrikOlsen]

Get what picture?
State your case in full please.

[Terry Giblin]

Get what picture?
State your case in full please.

All I have at present is a picture and an idea.

http://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Red_blue_circle.svg/200px-Red_blue_circle.svg.png

I am fairly confident now that "The fundamental theorem of ......" has something to do with Cauchy and Liouville's theorem, complex numbers and polynomials (in multi-dimensions), out of which 'natural prime numbers' appear.

Like they say "Only a 'natural constant' is bounded in a complex plane."

I am interested in the solutions on the 'real line' in a complex plane.

Call it brain storming, amongst friends.

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[kleindoofy]

... I am interested in the solutions on the 'real line' in a complex plane. ...
I know all the answers to that.

[HenrikOlsen]

All I have at present is a picture and an idea.
No, you showed a picture and told us to guess your idea based on the picture.

Could you please state explicitly what in the name of all cure furry creatures you're talking about?

[Terry Giblin]

No, you showed a picture and told us to guess your idea based on the picture.

Dear Henrik,

You are absolutely correct, its like

"Pin the tail on the donkey"

http://www.party-games.net/images/pin-the-tail-on-the-donkey-4.gif

[Image removed for being in violation of BAUT size rules] - The donkey always wins.


Assume the following diagram, represent 'X to the power N'.

Can you please 'point' to the all 'reals', in the diagram?

http://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Red_blue_circle.svg/200px-Red_blue_circle.svg.png

Or

http://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Red_blue_circle.svg/200px-Red_blue_circle.svg.png - Sorry I will not post this image again. - Point made.

It's neither Red or Blue.

Light in, Light out.

[Jim]

Terry Giblin, stop playing games. State your point/the purpose of this thread explicitly or ask that it be closed.

[Nowhere Man]

Too late.

Fred