List questions from real-analysis

Published on 13 Apr 2026 - 6:56

120

Views

limit points of $z^n$, where $z\in\mathbb{C}$,$n\in\mathbb{N}$, and $|z| = 1$.

Published on 15 Apr 2026 - 21:30

105

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Approximation of $f(x) = \max\left\{0,x\right\}$ using "dominate convergence theorem"

Published on 14 Apr 2026 - 2:19

104

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Stone-Weierstrass theorem applied in $L^2[0,1]$.

Published on 12 Apr 2026 - 22:10

73

Views

Prove that $T$ has a minimal set and list countably many minimal sets of $T$.

Published on 29 Apr 2026 - 12:53

25

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Killing a singularity

Published on 10 Apr 2026 - 18:03

324

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Big O notation: If $f=O(g)$ then $\int f=O(\int g)$?

Published on 16 Apr 2026 - 6:08

860

Views

Prove that $\sup(a+S)=a+\sup(S)$

Published on 16 Apr 2026 - 8:42

103

Views

Rolles theorem application

Published on 14 Apr 2026 - 22:17

396

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Show that a function is in the closed convex hull

Published on 12 Apr 2026 - 21:47

38

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proving piece wise function is discontinuous

Published on 16 Apr 2026 - 15:15

109

Views

Showing a function $f$ is improperly integrable on $[a,b)$ if $\lim\limits_{x\to b}\frac{f(x)}{g(x)}=L$ and $g$ is improperly intergrable

Published on 17 Apr 2026 - 14:48

129

Views

How can you find $\int_0^8xf'(x)\,{\rm d}x$ when $f(8) = 9$ and $f(4+x) = -f(4-x)$?

Published on 16 Apr 2026 - 11:31

339

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f is measurable function iff $f ^{-1} (A) $ is measurable for every finite set?

Published on 16 Apr 2026 - 5:22

206

Views

How to prove Favard Inequality?

Published on 10 Apr 2026 - 4:08

List Question

smooth envelope of the convex function

limit points of $z^n$, where $z\in\mathbb{C}$,$n\in\mathbb{N}$, and $|z| = 1$.

Approximation of $f(x) = \max\left\{0,x\right\}$ using "dominate convergence theorem"

Stone-Weierstrass theorem applied in $L^2[0,1]$.

Prove that $T$ has a minimal set and list countably many minimal sets of $T$.

Killing a singularity

Big O notation: If $f=O(g)$ then $\int f=O(\int g)$?

Prove that $\sup(a+S)=a+\sup(S)$

Rolles theorem application

Show that a function is in the closed convex hull

proving piece wise function is discontinuous

Showing a function $f$ is improperly integrable on $[a,b)$ if $\lim\limits_{x\to b}\frac{f(x)}{g(x)}=L$ and $g$ is improperly intergrable

How can you find $\int_0^8xf'(x)\,{\rm d}x$ when $f(8) = 9$ and $f(4+x) = -f(4-x)$?

f is measurable function iff $f ^{-1} (A) $ is measurable for every finite set?

How to prove Favard Inequality?

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