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domath
  • Member for 5 years, 3 months
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  • New Haven, CT, USA
5 votes
1 answer
907 views

Example of function of bounded variation

4 votes
0 answers
208 views

Application of Radon-Nikodym Theorem

4 votes
1 answer
120 views

The bilinear functional cannot be continuous on the space X

4 votes
1 answer
187 views

isolated point of spectrum of compact self-adjoint linear operator on infinite-dimensional separable Hilbert space.

3 votes
1 answer
127 views

simple Application of Gram-Schmidt Orthogonalization

3 votes
0 answers
37 views

Prove that for the defined $\langle .,. \rangle$ there exist $0 < a \le b$ such that $a\|x\| \le \|x\|_\ast ≤ b\|x\|$ for all $x \in H$.

3 votes
1 answer
69 views

show that there exists $f$ s.t. $\int_E(1-f)d\mu=\int_Efd\nu$

3 votes
2 answers
193 views

Riesz Representation and Ring Homomorphism

3 votes
1 answer
109 views

Show that $g(x) = \int_E f(x − t)d\lambda(t)$ is continuous on $\mathbb{R}$

3 votes
1 answer
202 views

Understanding Partition of Unity

3 votes
1 answer
271 views

the space of Lipschitz functions is complete metric space

3 votes
3 answers
96 views

proving that the function $f(x) = \lambda(S ∩ (S + x))$ is a continuous and $\lim_{x\to\infty} f(x) = 0$

3 votes
1 answer
185 views

If $f_n \to f$ a.e. , and $f_n$ bounded sequence ,then $f_n \to f$ weakly in $L^p(\mathbb{R})$ .

3 votes
0 answers
36 views

$E_{n,k}= \bigcup_{m\ge n} \Big\{x : |f_m(x)-f(x)|>\frac{1}{k}\Big\}$.Show that $\lim_{n\to \infty}m(E_{n,k})=0$

2 votes
1 answer
56 views

if $1 \le p_1 < p_2 < \infty$, $f_n \rightharpoonup f$ W-$L^{P_2}$ implies $f_n \rightharpoonup f$ weakly in $L^{P_1}$

2 votes
4 answers
76 views

polynomials in $t^2$ is dense in $C([a, b])$ if $0 \notin [a,b]$

2 votes
1 answer
87 views

Equivalent definition of sigma algebra

2 votes
0 answers
93 views

Extension Theorem; Lebesgue measure

2 votes
2 answers
155 views

Corollary of Borel-Cantelli lemma

2 votes
1 answer
46 views

understanding a proof of existence of a function on R

2 votes
2 answers
222 views

if $f \geq 0$ Lebesgue measurable the set $A := \{(x,y)\in \mathbb{R}^2 \mid 0 < y < f(x)\}$ is measurable - proof verification

2 votes
2 answers
712 views

Slice of a Borel set in $\mathbb{R}^2$ is Borel

2 votes
1 answer
363 views

If $E_1 \cup E_2$ is measurable with $λ^\ast(E_1 \cup E_2) = λ^\ast(E_1)+ λ^\ast(E_2)$, then $E_1$ and $E_2$ are measurable.

2 votes
1 answer
86 views

$\forall \epsilon>0 , \exists$ a finite linear combination of charactristic functions of intervals such that $\|f-\phi\|_{L^1}<\epsilon$.

2 votes
1 answer
215 views

Prove that $\sqrt{x}\sin\frac{\pi}{2\sqrt{x}}$ is not of bounded variation and is not Lipschitz

2 votes
2 answers
72 views

Example of continuity of measure and convergence in measure

2 votes
2 answers
373 views

Lebesgue measure in $\mathbb{R}^2$

2 votes
1 answer
134 views

if $\sum_{k=1}^\infty \|x_k\|$ converges , then $\sum_{k=1}^\infty x_k$ also converges.

2 votes
1 answer
156 views

Examples of compact operators, solution verification

2 votes
1 answer
51 views

General practice to find the operator norm