Intereting Posts

Prime ideals in $\mathbb{R}$
A question concerning the Cantor (ternary) function
Solvability of a system related to the subsets of {1,2,3}
Prove a (unital) ring with this property has no zero divisors?
Question from Folland Chapter 1 Exercise 14
$T$ is continuous if and only if $\ker T$ is closed
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
What does “$\mathbb{F^n}$ is a vector space over $\mathbb{F}$” mean?
Proof of Pythagorean theorem without using geometry for a high school student?
Prove that the exponential function is differentiable
Negative factors of a number
how to prove $\sum {\frac{1}{n^{1+1/n}}}$ is divergent
Is this function holomorphic at 0?
Does $\lim_{(x,y) \to (0,0)} \frac{x^4+y^4}{x^3+y^3}$ exist?
An application of Pigeon Hole Principle

Is there any difference between the two? I have not met any formal definition of the support of a random variable. I know that for the function $f$ the support is a closure of the set $\{y:\;y=f(x)\ne0\}$.

- Can the the radius of convergence increase due to composition of two power series?
- Existence of a section of non-zero measure
- Outer measure is countably subadditive
- Why does zero derivative imply a function is locally constant?
- Is the unit sphere in $(C, \| \cdot\|_1)$ compact?
- Is this two-dimensional version of the Intermediate Value Theorem correct?
- A consequence of the Mean Value Theorem for Integrals
- Can the product of two monotone functions have more than one turning point?
- Is there a monotonic function discontinuous over some dense set?
- Limit distributions for Markov chains $X\to\sqrt{U+X}$

The support of the probability distribution of a random variable $X$ is the set of all points whose every open neighborhood $N$ has the property that $\Pr(X\in N)>0$.

It is more accurate to speak of the support of the *distribution* than that of the support of the random variable.

The complement of the support is the union of all open sets $G$ such that $\Pr(X\in G)=0$. Since the complement is a union of open sets, the complement is open. Therefore the support is closed.

- Reflected rays /lines bouncing in a circle?
- Relationship between $\operatorname{ord}(ab), \operatorname{ord}(a)$, and $\operatorname{ord}(b)$
- Sufficient conditions for exchangeability of random variables
- Maximum Proof (Average?)
- Poisson's equation with Robin boundary conditions
- If a function $f(x)$ is Riemann integrable on $$, is $f(x)$ bounded on $$?
- Prove that $2730$ divides $n^{13} – n$ for all integers $n$.
- Proof Verification – Every sequence in $\Bbb R$ contains a monotone sub-sequence
- Algebraic equation problem – finding $x$
- Finding the heat flow across the curved surface of a cylinder
- Real integrals using Complex integration
- Interior $H^2$ regularity – applying “Cauchy's inequality with $\epsilon$”
- Simplifying a certain polylogarithmic sum in two variables
- What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?
- Formula and proof for the sum of floor and ceiling numbers