Question

Does any subset of $[0,1]$ have a well-defined Lebesgue Measure? No.

score 83 · Answer 1 · 2026-04-12 02:39:11

83

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Does any subset of $[0,1]$ have a well-defined Lebesgue Measure? No.

Published on 12 Apr 2026 - 2:39

score 228 · Answer 2 · 2026-04-14 22:20:51

228

Views

How to show that $m^(A\cap (\cup_{i=1}^\infty E_i))=\sum _{i=1}^\infty (m^(A\cap E_i))$

Published on 14 Apr 2026 - 22:20

score 31 · Answer 3 · 2026-04-15 04:18:26

31

Views

Orthonormal basis of a set, combined from two other sets.

Published on 15 Apr 2026 - 4:18

score 4.3k · Answer 4 · 2026-04-16 20:51:37

4.3k

Views

Prove that $m^(A\cup B)=m^(A)+m^*(B)$ whenever $\exists \alpha>0$ such that $|a-b|>\alpha$ for any $a\in A,b\in B$

Published on 16 Apr 2026 - 20:51

score 186 · Answer 5 · 2026-04-14 18:25:53

186

Views

How can I show that $f$ is continuous in $x_0$ iff $\mu(C_{x_0})=0$?

Published on 14 Apr 2026 - 18:25

score 1.5k · Answer 6 · 2026-04-16 07:26:58

1.5k

Views

Suppose that $f$ is continuous except at a finite number of points .Is $f$ measurable

Published on 16 Apr 2026 - 7:26

score 155 · Answer 7 · 2026-04-10 16:56:49

155

Views

Decomposition of Lebesgue's measure

Published on 10 Apr 2026 - 16:56

score 58 · Answer 8 · 2026-04-13 17:49:55

58

Views

Show that $\int _E f=0$ whenever $m(E)<\infty$

Published on 13 Apr 2026 - 17:49

score 59 · Answer 9 · 2026-04-11 18:47:24

59

Views

Does $A$ contain a set of positive measure that is symmetric about $(a+b)/2$?

Published on 11 Apr 2026 - 18:47

score 876 · Answer 10 · 2026-04-11 09:30:02

876

Views

Is Lebesgue outer measure continuous from above for sets with finite Lebesgue outer measure

Published on 11 Apr 2026 - 9:30

score 123 · Answer 11 · 2026-04-11 12:13:50

123

Views

How can I prove that $E$ is Lebesgue measurable (even if $\lambda^*(E)=\infty$)?

Published on 11 Apr 2026 - 12:13

score 157 · Answer 12 · 2026-04-15 21:36:28

157

Views

Show that $f,g$ is integrable.

Published on 15 Apr 2026 - 21:36

score 125 · Answer 13 · 2026-04-15 18:09:02

125

Views

Prove that the range of $f$ is contained in $[−1,1]$.

Published on 15 Apr 2026 - 18:09

score 84 · Answer 14 · 2026-04-11 17:45:46

84

Views

Question on Change of Variables

Published on 11 Apr 2026 - 17:45

score 37 · Answer 15 · 2026-04-16 18:40:34

37

Views

Calculate Volume of $S:= \{(x,y,z) \in \Bbb R^3 \mid z\gt 0, a^2 \lt x^2+y^2+z^2 \lt b^2, z^2 \lt c^2(x^2+y^2) \}$

Published on 16 Apr 2026 - 18:40

List Question

Does any subset of $[0,1]$ have a well-defined Lebesgue Measure? No.

How to show that $m^(A\cap (\cup_{i=1}^\infty E_i))=\sum _{i=1}^\infty (m^(A\cap E_i))$

Orthonormal basis of a set, combined from two other sets.

Prove that $m^(A\cup B)=m^(A)+m^*(B)$ whenever $\exists \alpha>0$ such that $|a-b|>\alpha$ for any $a\in A,b\in B$

How can I show that $f$ is continuous in $x_0$ iff $\mu(C_{x_0})=0$?

Suppose that $f$ is continuous except at a finite number of points .Is $f$ measurable

Decomposition of Lebesgue's measure

Show that $\int _E f=0$ whenever $m(E)<\infty$

Does $A$ contain a set of positive measure that is symmetric about $(a+b)/2$?

Is Lebesgue outer measure continuous from above for sets with finite Lebesgue outer measure

How can I prove that $E$ is Lebesgue measurable (even if $\lambda^*(E)=\infty$)?

Show that $f,g$ is integrable.

Prove that the range of $f$ is contained in $[−1,1]$.

Question on Change of Variables

Calculate Volume of $S:= \{(x,y,z) \in \Bbb R^3 \mid z\gt 0, a^2 \lt x^2+y^2+z^2 \lt b^2, z^2 \lt c^2(x^2+y^2) \}$

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