List questions from lebesgue-integral

Published on 12 Apr 2026 - 8:59

183

Views

Can $||f||_p$ tend toward infinity arbitrarily slowly?

Published on 17 Apr 2026 - 3:34

86

Views

Idea to show $\max\left\{\int_{0}^{1}\sqrt{1+n^2x^{2n-2}} \right\}dx < 2$

Published on 15 Apr 2026 - 16:12

53

Views

Is $f$ integrable under this conditions?

Published on 11 Apr 2026 - 5:20

169

Views

An integral giving back a function which is a factor in the integrand

Published on 10 Apr 2026 - 12:52

518

Views

Integrating against compactly supported continuous functions

Published on 10 Apr 2026 - 9:57

894

Views

Finding a sequence of functions which converge to the derivative of the Dirac delta

Published on 13 Apr 2026 - 17:02

110

Views

$\lim_{t \to 0} \frac1{t} \int_{\mathbb R} |f(x+t) -f(x)|dx=0 \implies f =0$

Published on 16 Apr 2026 - 4:01

582

Views

Lebesgue-Stieltjes integration by parts

Published on 16 Apr 2026 - 15:18

73

Views

measurable set and complement in $[0,1]$

Published on 13 Apr 2026 - 6:53

444

Views

Show that $\lim\limits_{n\to\infty}\int_{A}\sin(nx)dx = 0$ for any Lebesgue measurable $A \subseteq [0,1]$

Published on 15 Apr 2026 - 9:05

101

Views

Show that $\lim_{n\to\infty}\int_{-\pi}^{\pi}e^{ix}\cos(nx)dx = 0$

Published on 16 Apr 2026 - 0:08

221

Views

Is the map $x\mapsto\|x\|_p^p$, defined in $L^p[0,1]$ ($1<p<\infty$), strictly convex?

Published on 29 Apr 2026 - 18:18

84

Views

Constructing a $\sigma$-finite measure using measures of its subsets

Published on 12 Apr 2026 - 6:21

787

Views

Lebesgue's original definition of a measurable set?

Published on 13 Apr 2026 - 23:32

List Question

Show $\int_Af(x)\,dx=0$ for every measurable subset $A$ of $[0,1]$.

Can $||f||_p$ tend toward infinity arbitrarily slowly?

Idea to show $\max\left\{\int_{0}^{1}\sqrt{1+n^2x^{2n-2}} \right\}dx < 2$

Is $f$ integrable under this conditions?

An integral giving back a function which is a factor in the integrand

Integrating against compactly supported continuous functions

Finding a sequence of functions which converge to the derivative of the Dirac delta

$\lim_{t \to 0} \frac1{t} \int_{\mathbb R} |f(x+t) -f(x)|dx=0 \implies f =0$

Lebesgue-Stieltjes integration by parts

measurable set and complement in $[0,1]$

Show that $\lim\limits_{n\to\infty}\int_{A}\sin(nx)dx = 0$ for any Lebesgue measurable $A \subseteq [0,1]$

Show that $\lim_{n\to\infty}\int_{-\pi}^{\pi}e^{ix}\cos(nx)dx = 0$

Is the map $x\mapsto\|x\|_p^p$, defined in $L^p[0,1]$ ($1<p<\infty$), strictly convex?

Constructing a $\sigma$-finite measure using measures of its subsets

Lebesgue's original definition of a measurable set?

Trending Questions

Popular # Hahtags

Popular Questions