Question

$f$ Riemann int; $\exists$ cont. fcn. $g$ s.t $\int |f(x)-g(x)| dx < \epsilon$. Show supp $g$ can be taken to be arbitrarily small nbhd of supp $f$.

score 48 · Answer 1 · 2018-01-23 04:39:29

48

Views

$f$ Riemann int; $\exists$ cont. fcn. $g$ s.t $\int |f(x)-g(x)| dx < \epsilon$. Show supp $g$ can be taken to be arbitrarily small nbhd of supp $f$.

Published on 23 Jan 2018 - 4:39

score 200 · Answer 2 · 2018-01-23 05:18:39

By fundamental theorem of calculus, show that $f$ is odd if $\int_{-s}^sf(x)dx=0$, $\forall s\in \mathbb{R}$, $f$ being continuous function.

score 131 · Answer 3 · 2026-03-17 13:04:01

131

Views

Rudin's Riemann-Stieljes Integral Proof

Published on 17 Mar 2026 - 13:04

score 209 · Answer 4 · 2018-01-23 14:43:29

Give an example of a finction $f(x)$ such that $f(x)>0$ $\forall x\in[a,b]$, where $\sqrt{f}$ is Riemann integrable but $f$ is not.

score 41 · Answer 5 · 2026-03-17 11:17:49

41

Views

Stochastic proof variance

Published on 17 Mar 2026 - 11:17

score 85 · Answer 6 · 2018-01-23 19:26:37

85

Views

Showing that $g(x) = \begin{cases} f(x), & \ x \ne 0 \\ c, & \ x = 0 \end{cases}$ is Riemann integrable where $f$ is Riemann integrable

Published on 23 Jan 2018 - 19:26

score 1.2k · Answer 7 · 2026-03-20 04:32:02

1.2k

Views

Fubini's theorem for multiple Riemann integrals

Published on 20 Mar 2026 - 4:32

score 69 · Answer 8 · 2026-03-22 09:15:41

69

Views

$\int _0^ax\left(1-\frac{x}{a}\right)dx\:$ using Riemann Sums

Published on 22 Mar 2026 - 9:15

score 121 · Answer 9 · 2026-03-22 07:18:48

121

Views

Integral and discrete sum

Published on 22 Mar 2026 - 7:18

score 470 · Answer 10 · 2026-03-20 03:30:10

470

Views

Does this Riemann integral over $[0,1]^2$ exist?

Published on 20 Mar 2026 - 3:30

score 28 · Answer 11 · 2026-03-22 18:09:38

28

Views

Simplify $h(t) = \int_{0}^{1/t}f(u)\times dg^{(n)}\left(\frac{1}{u}\right)$

Published on 22 Mar 2026 - 18:09

score 93 · Answer 12 · 2018-01-28 19:04:37

93

Views

Let $f: [0,1] \to R$ be Riemann integrable, and let $a > 0$ be a real number. Show that $ f({x\over a})$ is Riemann integrable on $[0,a]$

Published on 28 Jan 2018 - 19:04

score 250 · Answer 13 · 2026-03-17 15:11:26

250

Views

Improper Integral Polynomial to negative exponent

Published on 17 Mar 2026 - 15:11

score 301 · Answer 14 · 2026-03-20 11:26:56

301

Views

Proof verification: a function with finitely many points of discontinuity is Riemann integrable

Published on 20 Mar 2026 - 11:26

score 122 · Answer 15 · 2026-03-25 01:20:30

122

Views

if the projection of $E\subseteq \mathbb{R}^n$ onto $\mathbb{R}^{n-1}$ has (n-1) dim. measure zero, then the set $E$ has $n$-dim. measure zero

Published on 25 Mar 2026 - 1:20

List Question

$f$ Riemann int; $\exists$ cont. fcn. $g$ s.t $\int |f(x)-g(x)| dx < \epsilon$. Show supp $g$ can be taken to be arbitrarily small nbhd of supp $f$.

By fundamental theorem of calculus, show that $f$ is odd if $\int_{-s}^sf(x)dx=0$, $\forall s\in \mathbb{R}$, $f$ being continuous function.

Rudin's Riemann-Stieljes Integral Proof

Give an example of a finction $f(x)$ such that $f(x)>0$ $\forall x\in[a,b]$, where $\sqrt{f}$ is Riemann integrable but $f$ is not.

Stochastic proof variance

Showing that $g(x) = \begin{cases} f(x), & \ x \ne 0 \\ c, & \ x = 0 \end{cases}$ is Riemann integrable where $f$ is Riemann integrable

Fubini's theorem for multiple Riemann integrals

$\int _0^ax\left(1-\frac{x}{a}\right)dx\:$ using Riemann Sums

Integral and discrete sum

Does this Riemann integral over $[0,1]^2$ exist?

Simplify $h(t) = \int_{0}^{1/t}f(u)\times dg^{(n)}\left(\frac{1}{u}\right)$

Let $f: [0,1] \to R$ be Riemann integrable, and let $a > 0$ be a real number. Show that $ f({x\over a})$ is Riemann integrable on $[0,a]$

Improper Integral Polynomial to negative exponent

Proof verification: a function with finitely many points of discontinuity is Riemann integrable

if the projection of $E\subseteq \mathbb{R}^n$ onto $\mathbb{R}^{n-1}$ has (n-1) dim. measure zero, then the set $E$ has $n$-dim. measure zero

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