Recent content by WannaBe22

Well... Z is obviously measurable...If A is also measurable then A \cup Z is also measurable... Hence, if A \cup Z is nonmeasurable , A must be nonmeasurable... So, if we take a nonmeasurable set A , containing all rational numbers, A-Q must also be nonmeasurable...But A-Q is a...

Well...After reading your guidance , I've tried taking the "Vitali Set" (The subset of [-0.5,0.5] which, for each real number r, contains exactly one number v such that v-r is rational )... If we'll denote this set as P, then we need to consider P \cup Q . P is nonmeasurable and contains...

Homework Statement Is there any non-Lebesgue-Measurable set A in R such as A contains all rational numbers? Homework Equations The Attempt at a Solution I've tried assuming that this is true... If such a set exists, then both A and A^c aren't countable... I've tried looking at A^c...

Thanks a lot! your guidance was very helpful!

Intuitively, f(x')- f(x) is measure of the portion of A between x and x' ... Intuitively , this whole thing seems quite trivial...But when I try to get to the formal aspect of the soloution (as seen in "The attempt at a solution" part) , everything messes out... How can I make the...

Homework Statement Let A \subseteq R be a Lebesgue-Measurable set. Prove that if the Lebesgue measure of A is less than infinity , then the function f(x) = \lambda(A \cap (-\infty,x)) is continous. Homework Equations The Attempt at a Solution I'm really confused about the definition of...

Homework Statement Prove the set A= \bigcup_{n=1}^{\infty} ( \frac{n}{5} , \frac{n}{5} + \frac{n+1}{2^n} ) is Lebesgue measurable and calculate its measure. Homework Equations The Attempt at a Solution I've proved the set is measurable...But how can I calculate its measure? I...

Homework Statement Let K = \{ (x,y) | -1<x<1 , -1<y<1 \} . Find the unique soloution of dirichlet problem: \Delta u(x,y) =0 , (x,y) \in K , u(x,y) = |x+y| , (x,y) \in \partial K . Homework Equations The Attempt at a Solution We need to guess a soloution and not use...

You mean that we need to add to the result for u^3 - f(y) for some function f? That is: u^3 = \frac{1}{-3ln(x) - 3c_2 +f(y)} If so, then because we have a singularity in ln(x) = -c_2 , I don't think we have any restrictions on this f... We'll have a singularity anyway... Am I right...

Homework Statement Let f(x,y) be the soloution of xu_x +yu_y = u^4 that is defined in the whole plane. Prove that f = 0 . Hint: Think of the characteristic curves of this PDE. HOPE You'll be able to help me Thanks in advance! Homework Equations The Attempt at a Solution...

Thanks a lot!

Homework Statement I'll be delighted to get an answer to the following question: Does every algebraic extension of a field is a simple extension? Homework Equations The Attempt at a Solution I'm pretty sure that the answer is negative... I was thinking on taking the field of all the...

You're right... I'm sry... I've corrected my typo

Homework Statement Mobius Transformation copies the annulus \{ z: r<|z|<1 \} to the region bounded by the discs \{ z : |z-\frac{1}{4}| = \frac{1}{4} \} and \{ z: |z|=1 \} . Find r Hope you guys will be able to help me! Thanks a lot! Homework Equations The Attempt at a...

I don't know how to solve the latex problems...It should write it ok... I don't know what I did wrong