Question

prove that for every integrable function $f(x)$ exists step function $h(x)$ such $ \intop_{a}^{b}|f\left(x\right)-h\left(x\right)|dx<\varepsilon $

score 753 · Answer 1 · 2020-06-01 16:36:02

753

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prove that for every integrable function $f(x)$ exists step function $h(x)$ such $ \intop_{a}^{b}|f\left(x\right)-h\left(x\right)|dx<\varepsilon $

Published on 01 Jun 2020 - 16:36

score 83 · Answer 2 · 2020-06-01 19:16:59

83

Views

Prove that if $ \lim_{x\to\infty}f\left(x\right)=L $ then $ \lim_{n\to\infty}\intop_{0}^{1}f\left(n\cdot x\right)dx=L $.

Published on 01 Jun 2020 - 19:16

score 88 · Answer 3 · 2020-06-01 19:21:58

88

Views

Does dominated Covergence Theorem hold for Riemann integral?

Published on 01 Jun 2020 - 19:21

score 39 · Answer 4 · 2026-03-26 06:25:27

39

Views

Estimation of a explicit Riemann-integral

Published on 26 Mar 2026 - 6:25

score 51 · Answer 5 · 2020-06-02 11:17:51

51

Views

A proof question using Riemann Lemma

Published on 02 Jun 2020 - 11:17

score 42 · Answer 6 · 2020-06-02 15:04:07

42

Views

Using definition of integration to prove

Published on 02 Jun 2020 - 15:04

score 103 · Answer 7 · 2020-06-02 20:26:41

103

Views

Verify the statements for Riemann-integrable function $f_n(x)$.

Published on 02 Jun 2020 - 20:26

score 165 · Answer 8 · 2026-03-27 16:46:15

165

Views

Upper and lower darboux sum

Published on 27 Mar 2026 - 16:46

score 25 · Answer 9 · 2026-03-27 20:12:54

25

Views

Integral of a non-negative continuous function on a closed bounded interval

Published on 27 Mar 2026 - 20:12

score 69 · Answer 10 · 2026-03-27 18:22:37

69

Views

Relation between an increasing function and its Riemann integral

Published on 27 Mar 2026 - 18:22

score 119 · Answer 11 · 2020-06-04 11:30:36

119

Views

Proof of Lebesgue criterion in Analysis 2 by Zorich

Published on 04 Jun 2020 - 11:30

score 52 · Answer 12 · 2026-02-24 10:17:12

52

Views

Checking the uniform convergence of sequence of functions

Published on 24 Feb 2026 - 10:17

score 100 · Answer 13 · 2026-03-28 21:51:43

100

Views

Evaluating: $\lim_{n\to \infty} \sum_{i=1}^n \frac{1}{\frac{an}{b-a}+i}$

Published on 28 Mar 2026 - 21:51

score 79 · Answer 14 · 2020-06-04 22:47:42

79

Views

Why does dominated convergence theorem not apply when $f_{n}(x) =1$ for rational $x$ and $f_{n}(x) = 0$ otherwise?

Published on 04 Jun 2020 - 22:47

score 41 · Answer 15 · 2020-06-05 09:19:57

41

Views

Decide if a function is Riemann Integrable

Published on 05 Jun 2020 - 9:19

List Question

prove that for every integrable function $f(x)$ exists step function $h(x)$ such $ \intop_{a}^{b}|f\left(x\right)-h\left(x\right)|dx<\varepsilon $

Prove that if $ \lim_{x\to\infty}f\left(x\right)=L $ then $ \lim_{n\to\infty}\intop_{0}^{1}f\left(n\cdot x\right)dx=L $.

Does dominated Covergence Theorem hold for Riemann integral?

Estimation of a explicit Riemann-integral

A proof question using Riemann Lemma

Using definition of integration to prove

Verify the statements for Riemann-integrable function $f_n(x)$.

Upper and lower darboux sum

Integral of a non-negative continuous function on a closed bounded interval

Relation between an increasing function and its Riemann integral

Proof of Lebesgue criterion in Analysis 2 by Zorich

Checking the uniform convergence of sequence of functions

Evaluating: $\lim_{n\to \infty} \sum_{i=1}^n \frac{1}{\frac{an}{b-a}+i}$

Why does dominated convergence theorem not apply when $f_{n}(x) =1$ for rational $x$ and $f_{n}(x) = 0$ otherwise?

Decide if a function is Riemann Integrable

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