# Alexander

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Undergratuate studen of mathematics.

# 145 Questions

 6 What is the topological properties of $\mathbb R$ that makes it uncountable (as compared to $\mathbb Q$)? 6 How to show that $\frac{x^2}{x-1}$ simplifies to $x + \frac{1}{x-1} +1$ 4 Holomorphically simply connected implies simply connected 3 For $f :\mathbb R \to \mathbb R$, there exists an $(a,b)$, such that $f$ is bounded on a sequence with limit $x$, for all $x\in(a,b)$ 3 Showing that $\int_x^{\infty}\frac{1}{u^2}e^{(-u^2/2)}du=\frac{1}{x}e^{(-x^2/2)}-\int_x^{\infty}e^{{(-u^2/2)}}du$

# 833 Reputation

 +10 What is the Lebesgue measure of the set of numbers in $[0,1]$ that has two thirds of ones in their infinite base-2 expansion? +10 If $\mathcal A$ generates $\mathcal S$ then $\sigma (X )=\sigma (X ^{-1 } ( \mathcal A ))$ +10 Show that iterated integral of indicator function over product space defines a countably additive (product) measure. +5 Example of topological space where there is a point and a subset $A$: $x \in \overline A$, but no sequence in $A$ converging to $x$?

 1 Equivalence of definition of measure concentrated on a set $A$ 0 If $f$ is right continuous at $c$, can I claim that $|sup _{x \in [c,x _i ]} f(x) -inf_{x \in [c,x _i ]}f(x)|<\epsilon$? 0 Is $\epsilon _{X_i}(I_n)$ an other notation for the indicator function?

# 57 Tags

 1 measure-theory × 31 0 probability-theory × 9 0 real-analysis × 39 0 complex-analysis × 8 0 general-topology × 18 0 probability × 8 0 calculus × 13 0 inequality × 8 0 elementary-set-theory × 12 0 sequences-and-series × 7

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 Mathematics 833 rep 410 Stack Overflow 101 rep Seasoned Advice 101 rep 1