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Etienne
  • Member for 9 years, 2 months
  • Last seen more than a month ago
32 votes
Accepted

Sequence of monotone functions converging to a continuous limit, is the convergence uniform?

16 votes
Accepted

Showing that $\sum_{k=0}^{\infty} a^{k} \cos(kx) = \frac{1- a \cos x}{1-2a \cos x + a^{2}}$ without using complex variables

15 votes
Accepted

If two Borel measures coincide on all open sets, are they equal?

13 votes

How to show that this limit is tend to zero?

12 votes
Accepted

integral computed with respect to a sub-$\sigma$-algebra

12 votes

True Or not: Compact iff every continuous function is bounded

11 votes
Accepted

Orthonormal Sets in Hilbert Spaces

11 votes
Accepted

Show that $\left(1+\dfrac{x}{n}\right)^n \to e^x$ as $n \to \infty$ in a normed ring $R$

11 votes
Accepted

Show that if $f$ is integrable on $[a,b]$, then $|f|$ is also integrable.

11 votes

if $AB\neq 0$ for any non zero matrix $B$ then $A$ is invertible

10 votes

Uniform convergence of sequence of convex functions

10 votes

in a topological space only finite subsets are compact sets

10 votes
Accepted

A counter example of best approximation

10 votes

Good text to start studying topological games?

9 votes
Accepted

Are "most" continuous functions also differentiable?

9 votes
Accepted

Is the function $f(z)=\frac{(\bar z)^2} z$ analytic at $0$? Is it continuous at $0$ and does it satisfy the Cauchy-Riemann equations?

9 votes
Accepted

Cantor Set and ternary expansions.

9 votes

Linear combinations of delta measures

9 votes
Accepted

Continuous function with linear directional derivatives=>Total differentiability?

8 votes
Accepted

Nonseparable $L^2$ space built on a sigma finite measure space

8 votes
Accepted

convolution of characteristic functions

8 votes
Accepted

Let $T: E \rightarrow E^*$ be a linear operator satisfying $\langle Tx,x \rangle \geq 0 \forall x \in E$. Prove T is bounded.

8 votes
Accepted

$f$ is approximated uniformly on $R$ by $p_n(x)$, then $f$ is a polynomial

8 votes

Interesting but short math papers?

8 votes

Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$

8 votes
Accepted

Can someone provide some examples to illustrate the difference between Pointwise equicontinuity and Uniform equicontinuity?

7 votes
Accepted

Extremely hard and stimulating (undergraduate) real analysis $problems$

7 votes
Accepted

Unitary elements in C*-algebras

7 votes

Assume that $ f ∈ L([a, b])$ and $\int x^nf(x)dx=0$ for $n=0,1,2...$.

7 votes
Accepted

$\forall t \in \mathbb{R}, e^{i \alpha_n t} \rightarrow 1 \implies \alpha_n \rightarrow 0$?

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