Question

Is every odd function on a symmetric interval of $\mathbb{R}$ lebesgue integrable?

score 141 · Answer 1 · 2020-11-10 18:50:09

141

Views

Is every odd function on a symmetric interval of $\mathbb{R}$ lebesgue integrable?

Published on 10 Nov 2020 - 18:50

score 71 · Answer 2 · 2020-11-10 23:17:28

71

Views

If $f$ is R-integrable, prove that if $\int_a^b |f(x)|dx = 0$, then $f(x) = 0$ for all $x\in[a,b]$. If this is not true, provide a counter-example.

Published on 10 Nov 2020 - 23:17

score 187 · Answer 3 · 2020-11-11 02:37:10

187

Views

$f$ is integrable $\iff$ for every sub-block $B$ we have that the function $f|_{B}$ is integrable, i.e. $\int_{A}f=\sum_{B}\int_{B}f|_{B}$

Published on 11 Nov 2020 - 2:37

score 698 · Answer 4 · 2020-11-11 10:25:00

698

Views

If $f$ is integrable on $[a,b]$ and $g$ is a function on $[a,b]$ . Show $g$ is integrable and $\int_a^b f(x) = \int_a^b g(x)$.

Published on 11 Nov 2020 - 10:25

score 141 · Answer 5 · 2020-11-12 15:00:08

141

Views

If $f(x) > 0$ and Riemann Integrable on $[a,b]$ is $\frac{1}{f(x)}$ Riemann integrable?

Published on 12 Nov 2020 - 15:00

score 93 · Answer 6 · 2026-04-01 14:19:05

93

Views

Where does the error lie here?

Published on 01 Apr 2026 - 14:19

score 135 · Answer 7 · 2026-03-26 02:55:42

135

Views

Doubts in question and solution about Jordan measurable sets and sets that has measure zero. Would you help me?

Published on 26 Mar 2026 - 2:55

score 212 · Answer 8 · 2020-11-18 22:50:18

212

Views

Integrability of generalization of Thomae's function on $[0,1] \times [0,1]$

Published on 18 Nov 2020 - 22:50

score 1.6k · Answer 9 · 2020-11-23 06:19:57

1.6k

Views

Prove function $f:[a, b] \rightarrow \mathbb{R}$ is Riemann integrable if and only if $f$ is bounded and almost everywhere continuous.

Published on 23 Nov 2020 - 6:19

score 173 · Answer 10 · 2020-11-24 10:00:54

173

Views

On integral of a function that is zero except on a measure zero set.

Published on 24 Nov 2020 - 10:00

score 34 · Answer 11 · 2026-04-01 05:09:14

34

Views

Could the limit be obtained by a Riemann sum?

Published on 01 Apr 2026 - 5:09

score 37 · Answer 12 · 2020-11-27 13:41:26

37

Views

Find upper sum to prove not Riemann integrability

Published on 27 Nov 2020 - 13:41

score 536 · Answer 13 · 2020-11-27 23:56:00

536

Views

Continuous function with a restriction is Riemann integrable

Published on 27 Nov 2020 - 23:56

score 75 · Answer 14 · 2020-11-28 06:20:43

75

Views

Proving two functions are equivalent given equal integrals without fundamental theorem of calculus

Published on 28 Nov 2020 - 6:20

score 62 · Answer 15 · 2026-04-01 05:05:48

62

Views

Show that $\bar\int f+g \leq \bar\int f + \bar\int g$

Published on 01 Apr 2026 - 5:05

List Question

Is every odd function on a symmetric interval of $\mathbb{R}$ lebesgue integrable?

If $f$ is R-integrable, prove that if $\int_a^b |f(x)|dx = 0$, then $f(x) = 0$ for all $x\in[a,b]$. If this is not true, provide a counter-example.

$f$ is integrable $\iff$ for every sub-block $B$ we have that the function $f|_{B}$ is integrable, i.e. $\int_{A}f=\sum_{B}\int_{B}f|_{B}$

If $f$ is integrable on $[a,b]$ and $g$ is a function on $[a,b]$ . Show $g$ is integrable and $\int_a^b f(x) = \int_a^b g(x)$.

If $f(x) > 0$ and Riemann Integrable on $[a,b]$ is $\frac{1}{f(x)}$ Riemann integrable?

Where does the error lie here?

Doubts in question and solution about Jordan measurable sets and sets that has measure zero. Would you help me?

Integrability of generalization of Thomae's function on $[0,1] \times [0,1]$

Prove function $f:[a, b] \rightarrow \mathbb{R}$ is Riemann integrable if and only if $f$ is bounded and almost everywhere continuous.

On integral of a function that is zero except on a measure zero set.

Could the limit be obtained by a Riemann sum?

Find upper sum to prove not Riemann integrability

Continuous function with a restriction is Riemann integrable

Proving two functions are equivalent given equal integrals without fundamental theorem of calculus

Show that $\bar\int f+g \leq \bar\int f + \bar\int g$

Trending Questions

Popular # Hahtags

Popular Questions