Question

Why it is not possible to construct a set function that is defined for all sets of real numbers with the following 3 properties?

score 122 · Answer 1 · 2026-04-12 16:20:15

122

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Why it is not possible to construct a set function that is defined for all sets of real numbers with the following 3 properties?

Published on 12 Apr 2026 - 16:20

score 532 · Answer 2 · 2026-03-26 16:56:44

532

Views

If a function has a jacobian with linearly independent columns on a set B, is the following union equal to B?

Published on 26 Mar 2026 - 16:56

score 369 · Answer 3 · 2026-03-25 09:29:02

369

Views

Continuity of the Lebesgue measure w.r.t the Hausdorff metric

Published on 25 Mar 2026 - 9:29

score 384 · Answer 4 · 2026-04-13 22:19:31

384

Views

Prove $\lim_{h\rightarrow0}m(E\Delta(E+h)) = 0$ for measurable set $E$ with finite measure

Published on 13 Apr 2026 - 22:19

score 68 · Answer 5 · 2026-04-10 15:49:03

68

Views

Lebesgue integrable for function

Published on 10 Apr 2026 - 15:49

score 112 · Answer 6 · 2026-04-15 21:38:58

112

Views

Show that $\lim_n f_n(x) = f(x)$ almost surely for an integrable function

Published on 15 Apr 2026 - 21:38

score 105 · Answer 7 · 2026-04-12 16:23:06

105

Views

nonnegative measurable function (monoton convergence theorem)

Published on 12 Apr 2026 - 16:23

score 403 · Answer 8 · 2026-04-12 20:58:32

403

Views

Every locally integrable function defines a Radon measure

Published on 12 Apr 2026 - 20:58

score 137 · Answer 9 · 2026-04-11 16:18:21

137

Views

Relation between Riemann integrable and Lebesgue integrable functions

Published on 11 Apr 2026 - 16:18

score 284 · Answer 10 · 2026-04-11 15:05:34

284

Views

How to check $f(x) = x^{-\alpha}, x \in (0,1]$ is Lebesgue integrable?

Published on 11 Apr 2026 - 15:05

score 471 · Answer 11 · 2026-04-09 00:13:00

471

Views

Proof of the change of variables formula without using the Monotone Convergence Theorem

Published on 09 Apr 2026 - 0:13

score 49 · Answer 12 · 2026-04-10 00:42:14

49

Views

Lebesgue integral on $[0,1]$ and alternating intervals

Published on 10 Apr 2026 - 0:42

score 98 · Answer 13 · 2026-04-11 02:25:16

98

Views

Probability of $X \in A$ using Lebesgue measure - proof verification

Published on 11 Apr 2026 - 2:25

score 92 · Answer 14 · 2026-04-13 23:46:27

92

Views

Derivability of convolution of a function with a finite measure

Published on 13 Apr 2026 - 23:46

score 128 · Answer 15 · 2026-04-13 03:45:55

128

Views

Showing Lebesgue Measurable Set is Measure Zero

Published on 13 Apr 2026 - 3:45

List Question

Why it is not possible to construct a set function that is defined for all sets of real numbers with the following 3 properties?

If a function has a jacobian with linearly independent columns on a set B, is the following union equal to B?

Continuity of the Lebesgue measure w.r.t the Hausdorff metric

Prove $\lim_{h\rightarrow0}m(E\Delta(E+h)) = 0$ for measurable set $E$ with finite measure

Lebesgue integrable for function

Show that $\lim_n f_n(x) = f(x)$ almost surely for an integrable function

nonnegative measurable function (monoton convergence theorem)

Every locally integrable function defines a Radon measure

Relation between Riemann integrable and Lebesgue integrable functions

How to check $f(x) = x^{-\alpha}, x \in (0,1]$ is Lebesgue integrable?

Proof of the change of variables formula without using the Monotone Convergence Theorem

Lebesgue integral on $[0,1]$ and alternating intervals

Probability of $X \in A$ using Lebesgue measure - proof verification

Derivability of convolution of a function with a finite measure

Showing Lebesgue Measurable Set is Measure Zero

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