Question

Some clarification needed on what it means for a $\sigma$-algebra to be generated, Borel $\sigma$-algebra

score 339 · Answer 1 · 2016-08-24 07:10:57

339

Views

Some clarification needed on what it means for a $\sigma$-algebra to be generated, Borel $\sigma$-algebra

Published on 24 Aug 2016 - 7:10

score 100 · Answer 2 · 2016-08-24 21:09:28

100

Views

Is the pointwise minimum of finitely many non-integrable, non-increasing functions non-integrable as well?

Published on 24 Aug 2016 - 21:09

score 165 · Answer 3 · 2016-08-27 09:54:55

165

Views

density,cumulative distribution, Lebesgue measure

Published on 27 Aug 2016 - 9:54

score 766 · Answer 4 · 2016-08-27 12:00:20

766

Views

Why is the Lebesgue integration definition for nonnegative functions well defined?

Published on 27 Aug 2016 - 12:00

score 201 · Answer 5 · 2016-08-27 16:14:51

201

Views

Well defined function on Lebesgue integration

Published on 27 Aug 2016 - 16:14

score 142 · Answer 6 · 2016-08-30 16:01:49

142

Views

Prove an identity regarding an integral operator

Published on 30 Aug 2016 - 16:01

score 24 · Answer 7 · 2016-08-30 22:05:36

24

Views

Showing finiteness of trigonometric lebesgue integral

Published on 30 Aug 2016 - 22:05

score 24 · Answer 8 · 2016-09-01 03:19:43

24

Views

Does this measure supported on "space covering" line segments converge to the Lebesgue measure?

Published on 01 Sep 2016 - 3:19

score 40 · Answer 9 · 2016-09-01 10:24:41

40

Views

computing $\int_{[a,b]}g^\sigma\mathrm{d}g$ for the increasing & continuous function $g$

Published on 01 Sep 2016 - 10:24

score 51 · Answer 10 · 2016-09-01 19:14:15

51

Views

Show $\Vert f\Vert_{L_1}=\Vert f\Vert_{L_2}=p$ on $[0,1]$ implies $f\equiv p$ a. e.

Published on 01 Sep 2016 - 19:14

score 166 · Answer 11 · 2016-09-02 08:02:05

166

Views

measure absolutely continuous with respect to the lebesgue measure for which $f_n \in L^1$ but $\{f_n\}$ does not converge

Published on 02 Sep 2016 - 8:02

score 874 · Answer 12 · 2026-03-25 17:24:36

874

Views

Can one define the Lebesgue integral with nonstandard analysis?

Published on 25 Mar 2026 - 17:24

score 128 · Answer 13 · 2016-09-02 17:19:06

128

Views

Is $f(x)=\begin{cases} \ \ \ \ \ \ \ \ \ x,\ \ \ \ x\in C \\ \frac{1}{x}\sin x, \ \ \ \ x\in[0,1]\setminus C\end{cases}$Lebesgue-integrable?

Published on 02 Sep 2016 - 17:19

score 862 · Answer 14 · 2016-09-03 21:09:05

862

Views

If $f \in L_p$ and $g \in L_\infty$, show that $fg \in L_p$.

Published on 03 Sep 2016 - 21:09

score 287 · Answer 15 · 2016-09-03 21:48:35

287

Views

Show that $f_n \to 0$ almost everywhere.

Published on 03 Sep 2016 - 21:48

List Question

Some clarification needed on what it means for a $\sigma$-algebra to be generated, Borel $\sigma$-algebra

Is the pointwise minimum of finitely many non-integrable, non-increasing functions non-integrable as well?

density,cumulative distribution, Lebesgue measure

Why is the Lebesgue integration definition for nonnegative functions well defined?

Well defined function on Lebesgue integration

Prove an identity regarding an integral operator

Showing finiteness of trigonometric lebesgue integral

Does this measure supported on "space covering" line segments converge to the Lebesgue measure?

computing $\int_{[a,b]}g^\sigma\mathrm{d}g$ for the increasing & continuous function $g$

Show $\Vert f\Vert_{L_1}=\Vert f\Vert_{L_2}=p$ on $[0,1]$ implies $f\equiv p$ a. e.

measure absolutely continuous with respect to the lebesgue measure for which $f_n \in L^1$ but $\{f_n\}$ does not converge

Can one define the Lebesgue integral with nonstandard analysis?

Is $f(x)=\begin{cases} \ \ \ \ \ \ \ \ \ x,\ \ \ \ x\in C \\ \frac{1}{x}\sin x, \ \ \ \ x\in[0,1]\setminus C\end{cases}$Lebesgue-integrable?

If $f \in L_p$ and $g \in L_\infty$, show that $fg \in L_p$.

Show that $f_n \to 0$ almost everywhere.

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