# Tagged Questions

24 views

### Finding the source for minimizer of a functional for all $C^2$-curve $x(t_0)=x_0$ and $x(t_1)=x_1$

I am trying to find where this problem comes from and it's corresponding proof for my students, but I cannot find the source anywhere. If anyone can find the source of this, or has any ideas where I ...
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### A class of function to study Fourier analysis, which is a subset of BV functions.

In Fourier analysis, while talking about pointwise convergence, we generally start with the class of functions called, BV functions (functions of bounded variation), which have a finite total ...
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### Bartle vs Rudin, which one is better for real analysis?

I'm in high school and I want to study real analysis, and I can choose between The elements of real analysis by Robert G. Bartle and Principles of mathematical analysis by Walter Rudin, so, from the ...
82 views

### Relation between the covers by sets of small diameter and the size of uniformly separated sets

Sorry I didn't find a better title. Here is the problem and my solution so far, I'd appreciate if someone could told me if is correct and for the last point, which at first sight seems to be ...
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### $\sin(x)$ is asymptotically equal to $x+5x^3$

Here is my question: I've never seen before this kind of fact underlined about asymptotic equalities (and why we keep only one term in these equalities) and I'm looking for reference. Here is an ...
205 views

### A question about a mathematical analysis book

I am a newcomer to Analysis. All knowledge I know about "Analysis" are differentials,limit and integration (basically, what we have been taught in high school) I am studying Principles of ...
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### Suggested book for self study.

I have a degree in Financial Risk Management, and did 4 semesters of calculus and analysis(but that was about 10 years back), with most of my other efforts going toward Mathematical Statistics and ...
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### Verification of sequence result

Is it true that if a real sequence $\{x_n\}_1^\infty$ has an infimum but no convergent subsequences then the infimum must be the minimum as well? Secondly, can it be proved that the sequence defined ...
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### Book recommendations for these types of math?

I'm planning to write a math olympiad in a couple of months (4-5), and am just really trying to get the preparation in. I'm a fairly good math student (did ok in math, not an A+, but I got an A so my ...
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### Expected values of continuous and bounded functions are equal then random variables are equal, too.

I have seen several of reasoning based on the following fact: Real random variables $X, Y$ in $\mathbb{R}^n$ are equal almost surely if and only if $\mathbb{E}g(X)f(X) = \mathbb{E} g(X)f(Y)$ for ...
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### Verification of extension result for Lipschitz functions

does anyone know the following result? If it holds in this form and any source which presents it? Thanks a lot. Consider metric space $(X,d_{X})$. Let $f:A \subset (X,d_{X}) \rightarrow \mathbb{R}$ ...
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### Is there a book only about epsilon delta proofs?

I want to know if there is such book, with beautiful epsilon delta proofs of all kind.