Question

Give me a example of a function Lebesgue Integrable over [a,b] that is not bounded in any subinterval of [a,b]

score 728 · Answer 1 · 2026-04-16 02:55:42

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Give me a example of a function Lebesgue Integrable over [a,b] that is not bounded in any subinterval of [a,b]

Published on 16 Apr 2026 - 2:55

score 315 · Answer 2 · 2026-04-09 22:42:32

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An application of Beppo Levi's Theorem

Published on 09 Apr 2026 - 22:42

score 1.6k · Answer 3 · 2026-04-11 15:10:32

1.6k

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Definition of the Lebesgue integral in terms of simple functions with finite measure support

Published on 11 Apr 2026 - 15:10

score 1.7k · Answer 4 · 2026-04-12 23:12:31

1.7k

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Showing that the integral of $x^nf(x)=0$ where $f$ is Lebesgue Integrable.

Published on 12 Apr 2026 - 23:12

score 298 · Answer 5 · 2026-04-09 22:25:41

298

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Measure Theory - condition for Integrability

Published on 09 Apr 2026 - 22:25

score 2.3k · Answer 6 · 2026-04-17 04:44:16

2.3k

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Showing that function is not Lebesgue Integrable in $[0,1]$

Published on 17 Apr 2026 - 4:44

score 103 · Answer 7 · 2026-04-15 11:13:40

103

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Why is $g_n:=\inf\{f_n,f_{n+1},...\}$ integrable if $f_n$ are?

Published on 15 Apr 2026 - 11:13

score 80 · Answer 8 · 2026-04-08 09:38:23

80

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An unknown function

Published on 08 Apr 2026 - 9:38

score 137 · Answer 9 · 2026-04-13 20:33:44

137

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Show that exists a function not increasing $f:(a,b)\rightarrow\mathbb{R}$ that is continuous only over $(a,b)\setminus D$

Published on 13 Apr 2026 - 20:33

score 2.5k · Answer 10 · 2026-04-13 16:57:11

2.5k

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Unbounded Lebesgue integrable functions

Published on 13 Apr 2026 - 16:57

score 6.6k · Answer 11 · 2026-04-11 16:06:46

6.6k

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Prove the Countable additivity of Lebesgue Integral.

Published on 11 Apr 2026 - 16:06

score 54 · Answer 12 · 2026-04-17 07:00:28

54

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Let $f_n \in C([0,2014]) $ Show, that if $f_n \rightrightarrows f$ and for all n $\int_{[0,2014]} ff_n dl_1=0$ then $ f\equiv 0$

Published on 17 Apr 2026 - 7:00

score 80 · Answer 13 · 2026-04-17 08:21:37

80

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Give examples of a basis of $L^1([0,1])$

Published on 17 Apr 2026 - 8:21

score 412 · Answer 14 · 2026-04-12 05:13:26

412

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Probabilistic Proof That An Absolutely Continuous Function is Differentiable Almost Everywhere

Published on 12 Apr 2026 - 5:13

score 80 · Answer 15 · 2026-04-17 06:34:38

80

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$\sup_{m \geq n} \, \operatorname{ess sup} |u_n - u_m| = \operatorname{ess sup} \, \sup_{m \geq n} |u_n - u_m|$

Published on 17 Apr 2026 - 6:34

List Question

Give me a example of a function Lebesgue Integrable over [a,b] that is not bounded in any subinterval of [a,b]

An application of Beppo Levi's Theorem

Definition of the Lebesgue integral in terms of simple functions with finite measure support

Showing that the integral of $x^nf(x)=0$ where $f$ is Lebesgue Integrable.

Measure Theory - condition for Integrability

Showing that function is not Lebesgue Integrable in $[0,1]$

Why is $g_n:=\inf\{f_n,f_{n+1},...\}$ integrable if $f_n$ are?

An unknown function

Show that exists a function not increasing $f:(a,b)\rightarrow\mathbb{R}$ that is continuous only over $(a,b)\setminus D$

Unbounded Lebesgue integrable functions

Prove the Countable additivity of Lebesgue Integral.

Let $f_n \in C([0,2014]) $ Show, that if $f_n \rightrightarrows f$ and for all n $\int_{[0,2014]} ff_n dl_1=0$ then $ f\equiv 0$

Give examples of a basis of $L^1([0,1])$

Probabilistic Proof That An Absolutely Continuous Function is Differentiable Almost Everywhere

$\sup_{m \geq n} \, \operatorname{ess sup} |u_n - u_m| = \operatorname{ess sup} \, \sup_{m \geq n} |u_n - u_m|$

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