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Alexander

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measure-theory

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140 Questions

Votes Activity Newest Views
4
8
votes
6
answers
2k
views

Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$ [duplicate]

algebra-precalculus inequality
Jul 31 '15 at 6:06 Aloizio Macedo♦ 30.3k
5
7
votes
2
answers
351
views

Can $\le$ be used insted of < in the definition of continuity?

real-analysis general-topology functional-analysis metric-spaces continuity
Aug 26 '16 at 12:12 Martin Sleziak 51.9k
2
7
votes
2
answers
189
views

What is the topological properties of $\mathbb R $ that makes it uncountable (as compared to $\mathbb Q $)?

general-topology real-numbers
Nov 6 '14 at 19:43 Pedro Tamaroff♦ 111k
 
7
votes
6
answers
407
views

How to show that $\frac{x^2}{x-1}$ simplifies to $x + \frac{1}{x-1} +1$

algebra-precalculus fractions
Feb 4 '14 at 18:46 Jeel Shah 8,336
 
6
votes
2
answers
841
views

How is Fubini's theorem used in the following proof?

real-analysis measure-theory fubini-tonelli-theorems
Sep 16 at 4:26 Calvin Khor 26.1k
 
5
votes
0
answers
611
views

Holomorphically simply connected implies simply connected

complex-analysis algebraic-topology
Jul 1 '14 at 6:15 Alexander 2,157
 
4
votes
0
answers
192
views

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?

measure-theory probability-theory lebesgue-measure
Dec 13 '14 at 8:12 Alexander 2,157
1
3
votes
3
answers
290
views

Show that if $fd'=f'd $ and the pairs $f, d $ and $f',d' $ are coprime, then $f=f' $ and $d=d' $.

elementary-number-theory
Feb 2 at 19:24 Bill Dubuque 245k
1
3
votes
2
answers
433
views

A probability function is determined on a dense set- Where is density used in the following proof?

measure-theory probability-theory
Dec 24 '14 at 11:37 Blackbird 1,755
1
3
votes
1
answer
170
views

Derive power series for $\frac{1}{1-x^2}$ from $\frac{1}{1-x}$?

calculus sequences-and-series power-series
Dec 23 '14 at 9:21 Martin Sleziak 51.9k
1
3
votes
1
answer
1k
views

Equivalence of definitions of measurable function: preimage of open set vs preimage of Borel set?

measure-theory
Nov 14 '14 at 10:10 Crostul 33.5k
1
3
votes
1
answer
36
views

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 $x\in(a,b)$

real-analysis general-topology analysis limits baire-category
Nov 3 '14 at 21:51 Yiorgos S. Smyrlis 74.4k
 
3
votes
1
answer
64
views

Show that $\displaystyle\int _{(0,1) \times (0,1)} \frac {xy } {(x^2+y^2)^2 } d(\mu \times \lambda )$ does not exist?

real-analysis measure-theory lebesgue-integral
Nov 3 '14 at 14:58 Squirtle 5,956
2
3
votes
1
answer
919
views

Equivalence of definition of measure concentrated on a set $A $

measure-theory
Oct 3 '14 at 10:06 Alexander 2,157
1
3
votes
1
answer
152
views

Give example where an outer measure is strictly less than the set function from which it is defined.

analysis measure-theory
Sep 26 '14 at 17:50 leo 9,148
 
3
votes
2
answers
2k
views

Show that $\sin z$ maps a specific set onto the upper-half plane.

complex-analysis
Aug 6 '14 at 19:49 next 400
 
3
votes
2
answers
66
views

Showing that $\int_x^{\infty}\frac{1}{u^2}e^{(-u^2/2)}du=\frac{1}{x}e^{(-x^2/2)}-\int_x^{\infty}e^{{(-u^2/2)}}du$

calculus integration improper-integrals
Dec 18 '13 at 17:47 Vishwa Iyer 1,662
 
3
votes
2
answers
153
views

Find the volume of $K=\{(x,y,z):|x-z^2|+|y-z^2|+z^2\le1\}$

multivariable-calculus integration volume
Jul 28 '13 at 22:53 Kaster 9,372
 
2
votes
5
answers
318
views

How to factor $8xy^3+8x^2-8x^3y-8y^2$

factoring
Oct 15 '16 at 18:47 Dietrich Burde 106k
 
2
votes
1
answer
66
views

Does $f _n \to f $ pointwise imply $f _n $ converges to $f $ in $L ^p $ norm if $\{f_n\}$ is Cauchy in $L^p$?

real-analysis measure-theory lp-spaces
Mar 17 '15 at 13:56 Jack D'Aurizio 327k
 
2
votes
1
answer
438
views

If $\mathcal A$ generates $\mathcal S$ then $\sigma (X )=\sigma (X ^{-1 } ( \mathcal A ))$

measure-theory probability-theory
Dec 11 '14 at 15:31 drhab 134k
 
2
votes
0
answers
121
views

Show that iterated integral of indicator function over product space defines a countably additive (product) measure.

measure-theory product-space
Nov 29 '14 at 21:34 Davide Giraudo 148k
 
2
votes
1
answer
68
views

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 $?

general-topology examples-counterexamples
Nov 25 '14 at 17:42 Asaf Karagila♦ 350k
 
2
votes
2
answers
43
views

Prove that $(\bigcup _{i=1 } ^{\infty } E _i )_x = \bigcup _{i=1 } ^{\infty } (E _i) _x $

measure-theory elementary-set-theory
Nov 17 '14 at 19:01 Asaf Karagila♦ 350k
 
2
votes
1
answer
520
views

Show that the product $\sigma $-algebra is generated by the $\pi $-system $\{B _1 \times B _2 : B \in \Sigma _1 , B _2 \in \Sigma _2 \} $

measure-theory elementary-set-theory
Nov 17 '14 at 18:37 drhab 134k
 
2
votes
1
answer
55
views

Show that $\lim _n (X \setminus E _n ) =(X \setminus \lim _n E _n )$, for $E_n $ an increasing sequence of sets

measure-theory elementary-set-theory
Nov 15 '14 at 17:46 Community♦ 1
1
2
votes
1
answer
105
views

Help with an inequality involving a convex function

real-analysis inequality convex-analysis
Nov 12 '14 at 10:51 Alexander 2,157
 
2
votes
2
answers
1k
views

Example of isolated point in Hausdorff space?

general-topology
Nov 1 '14 at 21:16 Fargle 1,277
 
2
votes
0
answers
111
views

Does Fubini's theorem imply $\int_X (\int _Y f _x d \lambda )d \mu=\int _X d \mu \int _Yf(x,y) d \lambda$?

real-analysis measure-theory
Oct 23 '14 at 14:29 Alexander 2,157
1
2
votes
1
answer
279
views

Help with proof of Jensens inequality

real-analysis measure-theory
Oct 14 '14 at 15:36 Some Math Student 1,442
1
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