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Etienne's user avatar
Etienne's user avatar
Etienne
  • Member for 11 years
  • Last seen more than 1 year ago
37 votes
Accepted

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

17 votes
Accepted

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

16 votes

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

How to show that this limit is tend to zero?

14 votes
Accepted

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

13 votes

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

12 votes
Accepted

Continuous function with linear directional derivatives=>Total differentiability?

12 votes

True Or not: Compact iff every continuous function is bounded

12 votes
Accepted

Are "most" continuous functions also differentiable?

11 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.

11 votes
Accepted

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

11 votes
Accepted

Cantor Set and ternary expansions.

11 votes
Accepted

A counter example of best approximation

11 votes
Accepted

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

10 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?

10 votes

Uniform convergence of sequence of convex functions

10 votes

Is a space where only finite subsets are compact sets always discrete?

10 votes
Accepted

Orthonormal Sets in Hilbert Spaces

10 votes

Good text to start studying topological games?

9 votes
Accepted

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

9 votes
Accepted

convolution of characteristic functions

9 votes

If two norms are equivalent on a dense subspace of a normed space, are they equivalent?

9 votes

Linear combinations of delta measures

9 votes
Accepted

Homework Problem: Complex Analysis Chain Rule

9 votes
Accepted

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

8 votes
Accepted

Two definitions of a bounded set in topological vector spaces

8 votes

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

8 votes

Interesting but short math papers?

8 votes
Accepted

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

8 votes
Accepted

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

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