Question

A sequence of absolutely continuous functions whose derivatives converge to $0$ a.e

score 552 · Answer 1 · 2026-03-21 08:31:41

552

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A sequence of absolutely continuous functions whose derivatives converge to $0$ a.e

Published on 21 Mar 2026 - 8:31

score 431 · Answer 2 · 2026-03-22 14:23:47

431

Views

Square Integrable Functions are Measurable?

Published on 22 Mar 2026 - 14:23

score 109 · Answer 3 · 2026-03-20 11:14:41

109

Views

Lebesgue measure and limit of the integral.

Published on 20 Mar 2026 - 11:14

score 82 · Answer 4 · 2026-03-24 02:13:01

82

Views

Solving an integral by using the Dominated Convergence Theorem.

Published on 24 Mar 2026 - 2:13

score 47 · Answer 5 · 2026-03-24 19:00:05

47

Views

Convergence of a seqence under the integral sign

Published on 24 Mar 2026 - 19:00

score 110 · Answer 6 · 2026-03-21 20:20:34

110

Views

If $g \in L^1$ and $f_n \to f$ a.e. where $|f_n| \leq 1$, then $gf_n \to gf$ uniformly on each compact set.

Published on 21 Mar 2026 - 20:20

score 504 · Answer 7 · 2026-03-20 03:45:50

504

Views

Integral with Dirac measure.

Published on 20 Mar 2026 - 3:45

score 84 · Answer 8 · 2026-03-22 04:19:44

84

Views

If $u \in \mathscr{L}^1(\lambda^n), v\in \mathscr{L}^\infty (\lambda^n)$, then $u \star v$ is bounded and continuous.

Published on 22 Mar 2026 - 4:19

score 88 · Answer 9 · 2026-03-22 18:21:19

88

Views

Proof that $x \mapsto \int |u(x+y)-u(y)|^p \lambda^n(dy)$ is continuous

Published on 22 Mar 2026 - 18:21

score 75 · Answer 10 · 2026-03-22 02:58:50

75

Views

a) Compute $T(1_{[\alpha,\beta]})$ for all $0<\alpha <\beta<0$

Published on 22 Mar 2026 - 2:58

score 126 · Answer 11 · 2026-03-24 05:43:34

126

Views

Lebesgue-integrating a non-Riemann integrable function

Published on 24 Mar 2026 - 5:43

score 240 · Answer 12 · 2026-03-17 11:30:12

240

Views

Evaluating $\int_{0}^{\infty} \frac {b \sin (ax) - a \sin (bx)}{x^2}dx$ for $a,b \gt 0$

Published on 17 Mar 2026 - 11:30

score 95 · Answer 13 · 2026-03-16 20:47:29

95

Views

A Rudin Counterexample. How can we show that $f$ is not measurable without Fubini?

Published on 16 Mar 2026 - 20:47

score 81 · Answer 14 · 2026-03-17 07:02:30

81

Views

Limit of $f_n(x)=f(x)(1+(sin x)^n)$

Published on 17 Mar 2026 - 7:02

score 78 · Answer 15 · 2026-03-17 16:07:10

78

Views

Evalute the Lebesgue integral $\int_{[0, 1]}f dm$

Published on 17 Mar 2026 - 16:07

List Question

A sequence of absolutely continuous functions whose derivatives converge to $0$ a.e

Square Integrable Functions are Measurable?

Lebesgue measure and limit of the integral.

Solving an integral by using the Dominated Convergence Theorem.

Convergence of a seqence under the integral sign

If $g \in L^1$ and $f_n \to f$ a.e. where $|f_n| \leq 1$, then $gf_n \to gf$ uniformly on each compact set.

Integral with Dirac measure.

If $u \in \mathscr{L}^1(\lambda^n), v\in \mathscr{L}^\infty (\lambda^n)$, then $u \star v$ is bounded and continuous.

Proof that $x \mapsto \int |u(x+y)-u(y)|^p \lambda^n(dy)$ is continuous

a) Compute $T(1_{[\alpha,\beta]})$ for all $0<\alpha <\beta<0$

Lebesgue-integrating a non-Riemann integrable function

Evaluating $\int_{0}^{\infty} \frac {b \sin (ax) - a \sin (bx)}{x^2}dx$ for $a,b \gt 0$

A Rudin Counterexample. How can we show that $f$ is not measurable without Fubini?

Limit of $f_n(x)=f(x)(1+(sin x)^n)$

Evalute the Lebesgue integral $\int_{[0, 1]}f dm$

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