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Bill
  • Member for 3 years, 11 months
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48 votes
6 answers
7k views

What is the intuition behind Chebyshev's Inequality in Measure Theory

7 votes
3 answers
324 views

if $f(x)\geq0$ for all $x$, then $f+f'+f''+f'''+ \cdots + f^n \geq0$ [duplicate]

6 votes
1 answer
382 views

If the image of an operator is closed, is the image of the powers of the operator also closed?

5 votes
1 answer
430 views

Understanding the proof of the Brezis-Lieb lemma

4 votes
1 answer
229 views

How do we use the dominated convergence theorem here? [duplicate]

4 votes
0 answers
287 views

Does irreducible over $\mathbb{R}$ imply irreducible over $\mathbb{Z}$?

4 votes
3 answers
448 views

How to show that the degree of this field extension is 12?

4 votes
3 answers
562 views

Proof that $\sqrt2$ is not in $Q(\pi)$

4 votes
2 answers
371 views

In a Banach Algebra, can the product of two elements be invertible if we know one of the element is non invertible?

4 votes
2 answers
292 views

Is a continuous function on compact convex set where the boundary is mapped to the set a self mapping?

4 votes
1 answer
76 views

How to show the norm of the difference of two pure state is 2?

4 votes
1 answer
352 views

How do we make sense of normal derivatives in PDE at boundary points?

4 votes
1 answer
349 views

Is the borel sigma algebra defined on the unit circle same as the borel algebra defined using the subspace topology?

4 votes
2 answers
820 views

Spivak's Proof that continuous differentiability implies differentiable

4 votes
2 answers
237 views

Prove a metric space is totally bounded iff it is bounded in every equivalent metric.

3 votes
2 answers
2k views

Suppose $AB=0$ for some non-zero matrix $B$. Can $A$ be invertible?

3 votes
2 answers
66 views

Is this theorem on product of metric spaces correct?

3 votes
1 answer
210 views

is there a mistake in this proof that union of finite nowhere dense sets is nowhere dense

3 votes
2 answers
916 views

If a sequence in a metric space does not have any convergent subsequence, then its range is closed

3 votes
1 answer
411 views

Do the position and velocity vectors live in the same space?

3 votes
3 answers
493 views

When proving several statements are equivalent, are we allowed to refer to a previous proved statement?

3 votes
0 answers
2k views

Why the definition of smooth boundary defined like this and how does it imply the interior ball property?

3 votes
1 answer
188 views

How to determine whether the following subsets are open, closed, or dense in the Zariski topology?

3 votes
1 answer
402 views

Why is an area preserving diffeomorphism a symplectomorphism (in $R^2$)

3 votes
1 answer
93 views

If $[F(a):F]=n$ and $p(x)$ is of degree $n$ with $a$ as a root, is it the minimal polynomial?

3 votes
1 answer
183 views

Prove if Hilbert dimension is finite, then the Hilbert space as a vector space has the same dimension

3 votes
1 answer
215 views

How to prove that the delta function is not actually a function

3 votes
3 answers
832 views

What are the connections between representation theory and differential equations?

3 votes
1 answer
129 views

How to show that the Hilbert-adjoint operator $T^*$ of a (not necessarily bounded) linear operator $T$ on a complex Hilbert space $H$ is bounded

3 votes
0 answers
226 views

Why does $f$ continuous and its Fourier coefficient converges absolutely implies the Fourier series converges uniformly?

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