Question

Can some transformation of a function always be found such that it has a specified integral?

score 36 · Answer 1 · 2019-02-14 10:14:53

36

Views

Can some transformation of a function always be found such that it has a specified integral?

Published on 14 Feb 2019 - 10:14

score 119 · Answer 2 · 2019-02-14 15:03:53

119

Views

$ \mu(|f|\geq \alpha) = \frac{1}{\alpha} ||f||_1$

Published on 14 Feb 2019 - 15:03

score 165 · Answer 3 · 2026-03-25 12:54:55

165

Views

Lindeberg CLT condition on Discrete Uniform independent sequence of random variables

Published on 25 Mar 2026 - 12:54

score 159 · Answer 4 · 2019-02-14 18:50:41

159

Views

Proving that the integral of a function with respect to a measure is finite when the measure is bounded

Published on 14 Feb 2019 - 18:50

score 77 · Answer 5 · 2019-02-15 07:59:45

77

Views

About the double integral and fubini's theorem

Published on 15 Feb 2019 - 7:59

score 247 · Answer 6 · 2019-02-15 10:59:17

247

Views

Prove that integral of infinite sum is in $L^1$

Published on 15 Feb 2019 - 10:59

score 177 · Answer 7 · 2019-02-16 16:59:21

177

Views

If $\Omega$ has finite measure and $f \in L^p(\Omega)$ then for $1 \leq q \leq p$ we have $f \in L^q(\Omega)$ and the following estimate.

Published on 16 Feb 2019 - 16:59

score 261 · Answer 8 · 2019-02-17 20:43:04

261

Views

Apply the Monotone Convergence Theorem to show that λ is countably additive.

Published on 17 Feb 2019 - 20:43

score 256 · Answer 9 · 2019-02-18 02:29:20

256

Views

Question on an example function (i.e. the "tent" function)

Published on 18 Feb 2019 - 2:29

score 1k · Answer 10 · 2026-03-27 13:46:04

1k

Views

Integrating continuous function of two variables by one of the variables, do I get continuous function?

Published on 27 Mar 2026 - 13:46

score 575 · Answer 11 · 2026-03-27 01:47:41

575

Views

Questions on the proof of $f*g\in C^\infty(\mathbb R)$ when $f\in L^2(\mathbb R)$ and $g\in C_c^\infty(\mathbb R)$

Published on 27 Mar 2026 - 1:47

score 199 · Answer 12 · 2019-02-19 10:05:53

199

Views

Given $\{f_k\}$, a sequence of bounded, complex-valued measurable functions, prove $\lim_{k \to \infty} \int_{\Omega} f_k dx = \int_{\Omega} f dx$

Published on 19 Feb 2019 - 10:05

score 80 · Answer 13 · 2026-03-27 01:46:44

80

Views

Showing that $f*\phi_t\to af$ in $\|\cdot\|_p$ as $t\to\infty$ with $f,\phi$ as given

Published on 27 Mar 2026 - 1:46

score 62 · Answer 14 · 2019-02-19 16:57:39

62

Views

Is my attempt at proving this corollary of the LDCT correct?

Published on 19 Feb 2019 - 16:57

score 51 · Answer 15 · 2019-02-20 18:09:42

51

Views

Let $ \Omega = \{ x \in \mathbb{R} : | x | \leq 1 \} $. Show that the function $ v(x) = |x|^{\alpha} $ belong to $ H^1(\Omega) $ if $ \alpha > 0 $

Published on 20 Feb 2019 - 18:09

List Question

Can some transformation of a function always be found such that it has a specified integral?

$ \mu(|f|\geq \alpha) = \frac{1}{\alpha} ||f||_1$

Lindeberg CLT condition on Discrete Uniform independent sequence of random variables

Proving that the integral of a function with respect to a measure is finite when the measure is bounded

About the double integral and fubini's theorem

Prove that integral of infinite sum is in $L^1$

If $\Omega$ has finite measure and $f \in L^p(\Omega)$ then for $1 \leq q \leq p$ we have $f \in L^q(\Omega)$ and the following estimate.

Apply the Monotone Convergence Theorem to show that λ is countably additive.

Question on an example function (i.e. the "tent" function)

Integrating continuous function of two variables by one of the variables, do I get continuous function?

Questions on the proof of $f*g\in C^\infty(\mathbb R)$ when $f\in L^2(\mathbb R)$ and $g\in C_c^\infty(\mathbb R)$

Given $\{f_k\}$, a sequence of bounded, complex-valued measurable functions, prove $\lim_{k \to \infty} \int_{\Omega} f_k dx = \int_{\Omega} f dx$

Showing that $f*\phi_t\to af$ in $\|\cdot\|_p$ as $t\to\infty$ with $f,\phi$ as given

Is my attempt at proving this corollary of the LDCT correct?

Let $ \Omega = \{ x \in \mathbb{R} : | x | \leq 1 \} $. Show that the function $ v(x) = |x|^{\alpha} $ belong to $ H^1(\Omega) $ if $ \alpha > 0 $

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