Question

Find a monotonously increasing function in the interval $[0,1]$ that is discontinuous at every point$ (x=1/n), n=[2,3...\infty]$

score 157 · Answer 1 · 2018-02-26 02:45:05

157

Views

Find a monotonously increasing function in the interval $[0,1]$ that is discontinuous at every point$ (x=1/n), n=[2,3...\infty]$

Published on 26 Feb 2018 - 2:45

score 253 · Answer 2 · 2026-03-25 05:02:14

253

Views

Prove that $\frac{\sin(x)}{1+|x|}$ is not Lebesgue integrable

Published on 25 Mar 2026 - 5:02

score 136 · Answer 3 · 2018-02-27 17:21:47

136

Views

Explain why discontinuous function is Riemann-Integrable

Published on 27 Feb 2018 - 17:21

score 59 · Answer 4 · 2018-02-27 21:04:56

59

Views

limit as $\delta \rightarrow 0 \int_{a + \delta}^{b} f(x)dx = \int_{a}^{b}f(x)dx$?

Published on 27 Feb 2018 - 21:04

score 165 · Answer 5 · 2018-02-28 19:49:39

165

Views

Example of primitive function which isn't Riemann-integrable on a closed interval [0,1]

Published on 28 Feb 2018 - 19:49

score 1.3k · Answer 6 · 2018-02-28 21:21:29

1.3k

Views

Example of bounded f:[0,1]->R which has primitive but not Riemann-integrability in closed interval?

Published on 28 Feb 2018 - 21:21

score 91 · Answer 7 · 2018-03-02 07:04:13

91

Views

Prove that $\int_{- \infty}^{\infty} f(x) dx = \int_{- \infty}^{\infty} f(-x) dx.$ (Analysis)

Published on 02 Mar 2018 - 7:04

score 60 · Answer 8 · 2018-03-02 22:22:26

60

Views

Real Analysis. Integration. Confused

Published on 02 Mar 2018 - 22:22

score 223 · Answer 9 · 2026-03-25 04:55:35

223

Views

Riemann-Lebesgue lemma applied

Published on 25 Mar 2026 - 4:55

score 211 · Answer 10 · 2018-03-04 10:41:04

211

Views

Give an example of a function having infinite number of point of discontinuities but integrable. Justify.

Published on 04 Mar 2018 - 10:41

score 2.9k · Answer 11 · 2018-03-04 11:30:04

2.9k

Views

If $f:[a,b]\to R$ is bounded with points of discontinuities enclosed by finite number of sub-intervals then $f$ is Riemann integrable on $[a,b]$.

Published on 04 Mar 2018 - 11:30

score 472 · Answer 12 · 2018-03-04 18:29:20

472

Views

Let $f : Q\to \mathbb{R}$ be bounded. Then the statement that $f$ is integrable over $Q$, with $\int_{Q}f = A$, is equivalent to the statement

Published on 04 Mar 2018 - 18:29

score 647 · Answer 13 · 2018-03-05 01:05:37

647

Views

Give an example of Riemann Integrable function which has a primitive. Justify

Published on 05 Mar 2018 - 1:05

score 143 · Answer 14 · 2026-03-25 05:00:02

143

Views

Why Volterra's function's derivative is zero on Cantor Set?

Published on 25 Mar 2026 - 5:00

score 118 · Answer 15 · 2026-03-25 05:01:33

118

Views

When are you allowed to say $\int_\mathbb{R} \mathbb{1}_{(0,1)}(x)x^{\alpha p}d\lambda = \int_0^1x^{\alpha p}dx$?

Published on 25 Mar 2026 - 5:01

List Question

Find a monotonously increasing function in the interval $[0,1]$ that is discontinuous at every point$ (x=1/n), n=[2,3...\infty]$

Prove that $\frac{\sin(x)}{1+|x|}$ is not Lebesgue integrable

Explain why discontinuous function is Riemann-Integrable

limit as $\delta \rightarrow 0 \int_{a + \delta}^{b} f(x)dx = \int_{a}^{b}f(x)dx$?

Example of primitive function which isn't Riemann-integrable on a closed interval [0,1]

Example of bounded f:[0,1]->R which has primitive but not Riemann-integrability in closed interval?

Prove that $\int_{- \infty}^{\infty} f(x) dx = \int_{- \infty}^{\infty} f(-x) dx.$ (Analysis)

Real Analysis. Integration. Confused

Riemann-Lebesgue lemma applied

Give an example of a function having infinite number of point of discontinuities but integrable. Justify.

If $f:[a,b]\to R$ is bounded with points of discontinuities enclosed by finite number of sub-intervals then $f$ is Riemann integrable on $[a,b]$.

Let $f : Q\to \mathbb{R}$ be bounded. Then the statement that $f$ is integrable over $Q$, with $\int_{Q}f = A$, is equivalent to the statement

Give an example of Riemann Integrable function which has a primitive. Justify

Why Volterra's function's derivative is zero on Cantor Set?

When are you allowed to say $\int_\mathbb{R} \mathbb{1}_{(0,1)}(x)x^{\alpha p}d\lambda = \int_0^1x^{\alpha p}dx$?

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