Recent content by simpleeyelid

MERCI beaucoup~~ I will check it..

Thanks and, could you tell me the name of this proposition?

Hello! I am having problems with the inverse function theorem. In some books it says to be locally inversible: first C1, 2nd Jacobian determinant different from 0 And I saw some books say to be locally inversible, it suffices to change the 2NDto "F'(a) is bijective".. How could these two be...

yeah, thanks, a lot, I finally find that it is convenient to construct it using the gluing lemma.

Hello! Could anybody give me an idea about this proof? knowing f_{i}:X\rightarrowR i=1,2 to show whether f_{3}=min{f_{1},f_{2}} is continuous! Thanks in advance, Regards

OK, thanks for this, really clear explanation, best wishes for you~

could we say that, since y=2x is a line in R², we have nothing to integrate? sorry that I am so unintuitive...

First, thanks very much indeed.. but, yes, honestly, not easy for me, I have to think about it... how to interpret this by saying the derivative of the signed measure does not exsit??

Could anyone help to give an example where in the same proba space, x and y have each the density function, while the joint density function does not exist? Thanks in advance, Best regards

OK, thanks for your answers, the 2nd one is OK now!

yes, that is what I am trying to do, however, it is strange that, some theorem in the book "Analysis and Mathematical physics" says the 2nd holds in C[a,b] wrt the second distance function, I am now quite confused...This is an original question from the book real analysis with economic applications.

Continuously differentiable Function C^1 {} \left[0,1\right] is complete with respect to the metric space D_\infty{}{f,g}=sup{\left|f(t)-g(t)\right|}+sup{\left|f^1{}(t)-g^1{}(t)\right|} but not in the d_\infty{}{f,g}=sup{\left|f(t)-g(t)\right|} Thanks for the helps in advance. Regards... BI