Recent content by ak416

ya you're right. I didn't account for the change of coordinates. thanks.

Homework Statement From the book Evans-PDE, p.24, equation (12), It is written that C ||D^2f||_{L_{\infty}(R^n)} \int_{B(0,\epsilon)}|\Phi(y)|dy \\ \leq \begin{cases} C \epsilon^2 |\log{}\epsilon| & (n=2) \\ C \epsilon^2 & (n \geq 3) \end{cases} How is this?Homework Equations \Phi(y) =...

Hi, can anyone give me an example of a bounded operator on a Hilbert space that has dense range but is not surjective? (Preferably on a separable Hilbert space) Im pretty sure such an operator exists since the open mapping theorem requires surjectivity and not just dense range, but its just...

So, just to extend my question, does anyone know of any Mathematical Physics programs out there that come with laboratory exposure or is this too much to ask for?

I am currently going into my 4th year of my undergraduate degree and I am looking at various possibilities for graduate school. I still haven't decided what my concentration will be but over the past 3 years I have acquired a pretty diverse background in economics, physics, math, and computer...

In R2 instead of intervals for the outer and inner measure, rectangles are used (higher dimensional rectangles are used for Rn, and for an arbitrary product of subsets of R we would use the basis elements of the product topology, i guess this is most natural) ok about your counterexample, B...

well from what i read in a more advanced textbook, is that a measure space is a set equipped with a measure function (with certain properties) that is defined on a sigma algebra (which defines the collection of measurable sets in the space). So ya, obviously, if you define the product measure in...

Spivak - Calculus. Starts from foundations and gets to some real advanced stuff. Exercises are difficult, but you know how it goes, whatever hurts you only makes you stronger...Just make sure youre strong in basic logic. Look for books in predicate logic, it will definitely help.

that was simple :)

Im wondering if its possible given x,y irrational, that x-y is rational (other than the case x=y). The reason I am asking this is that I am reading a book on measure theory and they try to construct a non measurable set and they start with an equivalence relation on [0,1} x~y if x-y is rational...

ok I am not so familiar with the formal definition of a measure space and the product measure. I was think more of something like this: given a finite number of non measurable sets in R (S1,...,Sn), their cartesian product is measurable ( By non measurable in R I mean the outer measure, m*S =...

finite cartesian product: http://en.wikipedia.org/wiki/Cartesian_product And if yes, what about countable products or arbitrary infinite products?

This is non measurable right?

Either Toronto or Waterloo. They are top in Math. I don't know much about Waterloo, but I do go to Toronto and I think it is perfect preparation if you want to go into grad school for Math/Physics. In your 4th year or even your 3rd year you can select from graduate level courses in such as...

no actually it says in my book that the standard middle thirds cantor set has measure zero, but not any cantor set. So I guess its incorrect.