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user119615
  • Member for 8 years, 7 months
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75 votes
10 answers
7k views

Why does being holomorphic imply so much about a function?

  • 3,511
64 votes
17 answers
15k views

Is the Law of Large Numbers empirically proven?

16 votes
3 answers
589 views

Generalization of $f(\overline{S}) \subset \overline{f(S)} \iff f$ continuous

  • 26.5k
11 votes
2 answers
237 views

Does there exist a number $n >1$ such that $n = s(n)^{s(n)}$?

9 votes
2 answers
725 views

Is there a set theory that avoids Russel's paradox while still allowing one to define the set of all sets not containing themselves?

8 votes
0 answers
1k views

Equivalent definitions of Lebesgue Measurability (Rudin and Royden)

  • 81
7 votes
2 answers
5k views

Prove $\lim_{x\rightarrow 0}\cos (x)=1$ with the epsilon-delta definition of limits

6 votes
4 answers
2k views

What is the motivation to build measure theory?

5 votes
2 answers
567 views

Can logic be defined in terms of sets? Can sets be defined using logic?

  • 241
4 votes
2 answers
3k views

Using Cauchy's Integral Theorem to evaluate integral?

  • 1,871
4 votes
2 answers
6k views

Convexity of functions and second derivative

4 votes
1 answer
2k views

$H$ and $K$ are subgroups of $G$. Show that $|HK|=|H||K|/|H\cap K|$. [closed]

4 votes
2 answers
313 views

intuition on why the density function of a normal law is$\frac{1}{\sqrt{2\pi \sigma^2 }}e^{-\frac{(x-\mu)^2}{2\sigma^2 }}$

  • 1,507
3 votes
1 answer
515 views

Tricky probability problem

  • 1,311
3 votes
0 answers
125 views

How to prove this ?

  • 31
3 votes
2 answers
58 views

$\varepsilon-\delta$ proof of $\lim_{x \to -\infty} \frac{1}{1+x}=0$

3 votes
3 answers
142 views

An equality in Hilbert spaces

  • 519
2 votes
1 answer
105 views

Prove function is compex analytic

2 votes
1 answer
79 views

A basic measure theory question on lebesgue integral

  • 1,959
2 votes
1 answer
641 views

Real analysis : Preliminary topics for - Measure Theory, Integration Theory, Differentiation and Integration [closed]

  • 195
2 votes
1 answer
57 views

Is it, in general, true that $\mu_f \leq \mu$, where $\mu_f, \mu$ are defined in the following way...

2 votes
0 answers
74 views

Measure $m=\mu$ if $\int fdm=\int fd\mu$

  • 7,278
1 vote
2 answers
2k views

Prove $\sup(|f|) - \inf(|f|) \leq \sup(f) - \inf(f)$ for bounded function $f$ on set $S$ [closed]

  • 809
1 vote
3 answers
749 views

Not losing money in a fair betting scheme?

1 vote
3 answers
2k views

How do we define equality in real numbers?

  • 1,236
1 vote
3 answers
125 views

rationalize the complex number multiplication rule

  • 2,663
1 vote
1 answer
888 views

Poisson process has independent and stationary increments

1 vote
2 answers
1k views

Convergence in probability implies convergence of characteristic functions

  • 1,274
0 votes
1 answer
204 views

Determine whether $f_n(x) = \frac {nx}{1+(nx)^2}$ is cauchy in $[ C^0([−1, 1], \mathbb {R} ), d_\infty]$

0 votes
2 answers
121 views

Do all the properties of exponents work for every real exponent? [closed]