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7 votes
1 answer
154 views

A technical lemma on linear combinations.

5 votes
2 answers
77 views

A particular function of $L^1$

4 votes
2 answers
222 views

The dual of $L^p(X,\mu)$, where $1<p<\infty$ and $\mu$ is a positive measure

4 votes
0 answers
41 views

A series of questions on the subspace generated in a Hilbert space.

4 votes
1 answer
57 views

A very important measure.

4 votes
3 answers
132 views

Is $\sum_{(n,k)\in\Bbb{N}\times\Bbb{N}}a_{n,k}=\sum_{n\in\Bbb{N}}\sum_{k\in\Bbb{N}}a_{n,k}$ a definition or a theorem?

4 votes
1 answer
95 views

Preliminary lemma to Hahn's decomposition theorem

3 votes
2 answers
186 views

A ball in a particular open set.

3 votes
1 answer
213 views

Equivalent definition of essential supremum

3 votes
1 answer
66 views

Ternary sequence

3 votes
1 answer
255 views

An easy question about the separability of $L^p(X,\mathcal{A}, \mu)$ space, where $p\in [1,+\infty)$

2 votes
1 answer
74 views

Two false equalities

2 votes
2 answers
119 views

Rudin real and complex analysis: looking for an observation

2 votes
2 answers
73 views

An inequality: from the complex to the real case.

2 votes
1 answer
146 views

Riesz- Fischer Theorem

2 votes
2 answers
67 views

Computation of an integral in a consequence of the Jensen's inequality.

2 votes
1 answer
58 views

On the norm of operator: Is it a closed set?

2 votes
0 answers
57 views

Multinomial theorem and differential of a function.

2 votes
1 answer
39 views

From definition of Cauchy sequence to definition of limit.

2 votes
1 answer
71 views

On the union of half-open intervals.

2 votes
0 answers
73 views

Definition of support in Evans book partial differential equation.

2 votes
1 answer
80 views

Limit of $u(x):=\int_{\mathbb{R}^n}\frac{f(y)}{|x-y|^{n-2}}\; dy.$

2 votes
0 answers
59 views

Proving that $f(x)=\begin{cases}\frac{\sin x}x&\text{if }x>0\\1&\text{if }x=0\end{cases}$ is not in $L^1([0,\infty))$

2 votes
2 answers
185 views

Reflexivity is invariant under isomorphism [closed]

2 votes
1 answer
37 views

Understanding $\int_{[0,1)}x^2d\mu=\frac13+\sum_{n=1}^\infty\frac1{n^2}$, where $\mu=m+\sum_{n=1}^\infty\delta_{1/n}$ and $m$ is the Lebesgue measure

2 votes
1 answer
291 views

Essential supremum is actually a minimum

2 votes
0 answers
94 views

Existence of the limit $\lim_{R\to\infty} \int_0^R \frac{\sin x}{x}\; dx$

2 votes
0 answers
19 views

Convergence of a sequence to a $\sup$ in a signed measure space.

1 vote
1 answer
117 views

About the Hahn Decomposition Theorem from J.Yeh Real Analysis.

1 vote
1 answer
57 views

Non-uniqueness of the extension in the Hahn-Banach Theorem for normed spaces and a question about a final consideration.

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