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Cauchy's Sequence's user avatar
Cauchy's Sequence
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6 votes

Find the derivative of a difficult integral

3 votes
Accepted

For Lebesgue integral theory, whether an integrable sequence of functions converging a.e. converges in L1 under a given "integral finite condition"

2 votes

Strong Law of Large Numbers for increasing index sets

2 votes

Limit of matrix expression $\lim_{B \to A} {(A - B)}^{-1} (A^2 - B^2)$

2 votes
Accepted

Decomposition of a closed set into a perfect set and an at most countable set is unique.

2 votes

Proof explanation: If $a\equiv b\pmod {p^n}$, then $a^p\equiv b^p\pmod {p^{n+1}}$

2 votes
Accepted

No identity for convolution (without Fourier)

1 vote

If $f$ is a convex increasing function, then $\lim_{x\rightarrow -\infty} \frac{1}{x}\int_{x}^{x_0}f(t)dt=-\lim_{x\rightarrow -\infty}f(x)$

1 vote

Show that $P$ is normal if and only if it is an orthogonal projection.

1 vote

Find Lebesgue measurable sets such that the measure of intersection is product of measures.

1 vote

Can we change the definition of negative exponents?

1 vote
Accepted

$\{ f\in C[0,1]:\exists K: |f(x)|\leq Kx\}$ is closed

0 votes

How to find the derivative of a definite integral where one of the limits is itself an integral

0 votes

Show that $F(x)=\begin{cases}x^2\sin(x^{-6/5}) &x\ne 0\\ 0 &x=0 \end{cases}$ is absolutely continuous on $[-1,1]$.

0 votes
Accepted

Alternative proof that the weak gradient is $0$ a.e. on level sets

0 votes
Accepted

Covering a countable metric space with finitely many subsets of bounded diameter

0 votes

Why do limits results change with algebraic manipulation?