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Lázaro Albuquerque's user avatar
Lázaro Albuquerque's user avatar
Lázaro Albuquerque's user avatar
Lázaro Albuquerque
  • Member for 10 years, 9 months
  • Last seen this week
5 votes
Accepted

$C^{1}([0,1])$ is dense in $C([0,1])$

3 votes

Show that $f$ is continuous if is $BV$ and has the ivp.

3 votes
Accepted

Confused with proof exercise real analysis

3 votes
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Existence of $\lim \frac{f(x)}{x}$ when $f \in C[0,+\infty)$, $f(x) \ge 0$ and $f(x+y) \le f(x) + f(y)$.

3 votes
Accepted

For each $n,n>0$ let $a_n$ be the number of points of intersection of the graph $y =\sin x$ with line $y= x/n$. Then the sequence $a_n$ is :

3 votes
Accepted

Hausdorff metric and compactness

3 votes

Limit function of uniform convergent bounded sequences is bounded

3 votes
Accepted

is it possible for a function continuous everywhere and differentiable nowhere have a finite arc length between two points?

3 votes
Accepted

Prove that the Fredholm Integral Equation is a contraction

2 votes

Let $A=\{(x,y) \in \Bbb R^2 \mid x \ge 1, 0<y<\frac{1}{x^2}\}$. Show that $m_2(A) < \infty$ where $m$ is the Lebesgue measure.

2 votes

Inverse function $f^{-1}:f(\mathbb{R})\to\mathbb{R}$ of a strictly increasing function $f:\mathbb{R}\to\mathbb{R}$ is continuous

2 votes
Accepted

Proving that if derivative of f(x) = a with a>0, f(x) must go to infinity

2 votes

$|\max_x f(x) - \max_x g(x)| \le \max_x |f(x) - g(x)|$ is it true?

2 votes

Is this approach for this particular question correct

2 votes
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Giving a formula for an integral and showing whether it can integrated

2 votes
Accepted

Rudin theorem 9.21 converse part proof

2 votes
Accepted

Show that $d(x_0, y_0) \le \epsilon/(1- \min(c,c'))$. Thus nearby contractions have nearby fixed points.

2 votes
Accepted

How to show that $f(x) = \text{sup}_{ i \in I}f_i(x)$ is measurable?

2 votes
Accepted

Kreyszig's FA Prob. $6$ section $2.8$

2 votes
Accepted

Proving an inequality involving absolute values

2 votes

Proof of $\sup AB=\max\{\sup A\sup B,\sup A\inf B,\inf A\sup B,\inf A\inf B\}$

2 votes
Accepted

How many inner products exist in $R^n$?

2 votes

$G$ is a non-abelian finite group.$f$ is an automorphism of $G$ such that $f^2 = I_G$.Show $f(x) = x$ for some $x \neq e$.

2 votes

$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$

2 votes

Recommended books that discuss the Fundamental Theorem of Algebra?

2 votes
Accepted

Another version of the chain rule

1 vote

A density proof not via Stone-Weierstrass

1 vote

Prob. 11, Chap. 3, in Baby Rudin: If $a_n > 0$ and $\sum a_n$ diverges, then how do we show that $\sum \frac{a_n}{1+a_n}$ too diverges?

1 vote
Accepted

A question involving a Borel probability measure

1 vote
Accepted

Convergence with respect to a specific norm implied by convergence in measure