Question

measure theory f$\in$ $L^1([0,1])$ then $\lim_{n\to \infty}$ (f, $\chi_n$) = 0

score 59 · Answer 1 · 2026-04-16 01:50:01

59

Views

measure theory f$\in$ $L^1([0,1])$ then $\lim_{n\to \infty}$ (f, $\chi_n$) = 0

Published on 16 Apr 2026 - 1:50

score 54 · Answer 2 · 2026-04-15 20:38:45

54

Views

Let $f$ be absolutely continuous on $[0,a]$ for all $a>0$ and $f(0)=0$ the show that $\int_{0}^{x}|f(t)f'(t)|\leq\frac{1}{2}(\int_{0}^{x}|f'(t)|)^2$.

Published on 15 Apr 2026 - 20:38

score 47 · Answer 3 · 2026-04-15 06:04:08

47

Views

if $f_n$ is point wise bounded measurable sequence then it is uniformly bounded on certain sets in $[0,1]$

Published on 15 Apr 2026 - 6:04

score 61 · Answer 4 · 2026-04-11 20:23:18

61

Views

Essential range and equality under composition

Published on 11 Apr 2026 - 20:23

score 412 · Answer 5 · 2026-04-08 20:47:38

412

Views

measure theory: how does a function f in L1 induces a measure?

Published on 08 Apr 2026 - 20:47

score 167 · Answer 6 · 2026-04-14 08:41:51

167

Views

A question regarding the existence of a differentiable function with certain simple measure-theoretic properties

Published on 14 Apr 2026 - 8:41

score 80 · Answer 7 · 2026-04-11 21:08:04

80

Views

How Lebesgue sigma algebra is different from outer regularity.

Published on 11 Apr 2026 - 21:08

score 135 · Answer 8 · 2026-04-16 10:11:47

135

Views

let $p$ be a real non-constant polynomial, prove that $\lim_{n \to \infty}\int_{0}^{1} e^{2\pi i n p(x)}dx=0$.

Published on 16 Apr 2026 - 10:11

score 145 · Answer 9 · 2026-04-06 02:53:04

145

Views

Prove The Identity Using Tonelli's or Fubini's Theorem

Published on 06 Apr 2026 - 2:53

score 206 · Answer 10 · 2026-04-12 01:07:29

206

Views

Laplace Transformation for measurable functions

Published on 12 Apr 2026 - 1:07

score 203 · Answer 11 · 2026-04-16 07:18:46

203

Views

(Excercise 11.17 in Baby Rudin) Why the integral $\int_{E} \sin n x dx$ is the imaginary part of the Fourier coefficient?

Published on 16 Apr 2026 - 7:18

score 173 · Answer 12 · 2026-04-16 09:54:02

173

Views

If $g:[a,b]\to[0,\infty]$ is lebesgue integrable on the compact interval $[a,b]$, is $g$ bounded $\textit{almost everywhere}$?

Published on 16 Apr 2026 - 9:54

score 245 · Answer 13 · 2026-04-16 10:22:57

245

Views

Show that if $\int fh < \infty$ for all $h \in L^q$ then $f \in L^p$

Published on 16 Apr 2026 - 10:22

score 144 · Answer 14 · 2026-04-16 11:45:50

144

Views

$f, g$ are continuous functions on $E$ where $E$ is measurable set. If $f=g$ a.e on $E$ then $f=g$ on $E$?

Published on 16 Apr 2026 - 11:45

score 141 · Answer 15 · 2026-03-25 12:25:31

141

Views

A set with positive Lebesgue Measure and not Borel measurable

Published on 25 Mar 2026 - 12:25

List Question

measure theory f$\in$ $L^1([0,1])$ then $\lim_{n\to \infty}$ (f, $\chi_n$) = 0

Let $f$ be absolutely continuous on $[0,a]$ for all $a>0$ and $f(0)=0$ the show that $\int_{0}^{x}|f(t)f'(t)|\leq\frac{1}{2}(\int_{0}^{x}|f'(t)|)^2$.

if $f_n$ is point wise bounded measurable sequence then it is uniformly bounded on certain sets in $[0,1]$

Essential range and equality under composition

measure theory: how does a function f in L1 induces a measure?

A question regarding the existence of a differentiable function with certain simple measure-theoretic properties

How Lebesgue sigma algebra is different from outer regularity.

let $p$ be a real non-constant polynomial, prove that $\lim_{n \to \infty}\int_{0}^{1} e^{2\pi i n p(x)}dx=0$.

Prove The Identity Using Tonelli's or Fubini's Theorem

Laplace Transformation for measurable functions

(Excercise 11.17 in Baby Rudin) Why the integral $\int_{E} \sin n x dx$ is the imaginary part of the Fourier coefficient?

If $g:[a,b]\to[0,\infty]$ is lebesgue integrable on the compact interval $[a,b]$, is $g$ bounded $\textit{almost everywhere}$?

Show that if $\int fh < \infty$ for all $h \in L^q$ then $f \in L^p$

$f, g$ are continuous functions on $E$ where $E$ is measurable set. If $f=g$ a.e on $E$ then $f=g$ on $E$?

A set with positive Lebesgue Measure and not Borel measurable

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