Question

Exercise 18 on p.39 in Exercises 2B in "Measure, Integration & Real Analysis" by Sheldon Axler.

score 104 · Answer 1 · 2023-03-13 03:45:18

104

Views

Exercise 18 on p.39 in Exercises 2B in "Measure, Integration & Real Analysis" by Sheldon Axler.

Published on 13 Mar 2023 - 3:45

score 25 · Answer 2 · 2023-03-23 12:00:46

25

Views

$\forall r>0,j=1,2,\ldots:\mu(\partial B(x_j,r))=0$ for a Borel probability measure $\mu$ over a metric space $X$ where $x_j$ are countably dense

Published on 23 Mar 2023 - 12:00

score 74 · Answer 3 · 2026-03-25 15:42:11

74

Views

Arbitrary union of measure $0$ open sets has measure $0$ in a separable metric space

Published on 25 Mar 2026 - 15:42

score 53 · Answer 4 · 2023-03-28 14:29:48

53

Views

If $B$ is a Borel set s.t. $\mu(\partial B)=0$ and $\lim_n\mu_n(B)=\mu(B)$ then does $\lim_n\mu(\overline{B}^{1/n}\setminus\overline{B})=0$ hold?

Published on 28 Mar 2023 - 14:29

score 57 · Answer 5 · 2023-03-29 13:42:11

57

Views

Calculating a lower bound of Lebesgue measure of some Borel set

Published on 29 Mar 2023 - 13:42

score 59 · Answer 6 · 2023-04-15 13:03:30

59

Views

A detail on the Polar Coordinate Theorem proof

Published on 15 Apr 2023 - 13:03

score 31 · Answer 7 · 2026-03-25 14:26:10

31

Views

Borel Measurability of a subset of $R^{\infty}$

Published on 25 Mar 2026 - 14:26

score 41 · Answer 8 · 2023-04-29 07:35:24

41

Views

regarding measurability of functions

Published on 29 Apr 2023 - 7:35

score 286 · Answer 9 · 2023-04-30 16:58:20

286

Views

Does a set of positive outer measure contain a measurable set of positive measure?

Published on 30 Apr 2023 - 16:58

score 81 · Answer 10 · 2026-02-23 17:27:25

81

Views

How can I prove that if $\int_{[0,1]} f~d\nu\leq C\int_{[0,1]} f~d\mu$ then the measures are absolutely continuous?

Published on 23 Feb 2026 - 17:27

score 39 · Answer 11 · 2023-05-02 22:23:56

39

Views

Borel measure - unbounded sets

Published on 02 May 2023 - 22:23

score 133 · Answer 12 · 2023-05-05 12:26:55

133

Views

proove that $\forall x \in X : \forall \epsilon > 0 : \exists \delta > 0 \text{ s.t. } \mu(B(x,\delta)) ≤ \epsilon$

Published on 05 May 2023 - 12:26

score 49 · Answer 13 · 2023-05-15 06:17:39

49

Views

Is $\mu_U(E) := \mu(E\cap U)$ a Radon measure when $U$ is open?

Published on 15 May 2023 - 6:17

score 169 · Answer 14 · 2023-05-17 01:14:08

169

Views

About the definition of a Borel measurable function in "Measure, Integration & Real Analysis" by Sheldon Axler.

Published on 17 May 2023 - 1:14

score 64 · Answer 15 · 2023-05-23 11:08:28

64

Views

If $f,g$ are two measurable functions on $[0,1]$ such that $\int_A f=\int_A g$ for all $A\subset[0,1]$ such that $\mu(A)=1/3$. Then $f=g$ a.e. $\mu$

Published on 23 May 2023 - 11:08

List Question

Exercise 18 on p.39 in Exercises 2B in "Measure, Integration & Real Analysis" by Sheldon Axler.

$\forall r>0,j=1,2,\ldots:\mu(\partial B(x_j,r))=0$ for a Borel probability measure $\mu$ over a metric space $X$ where $x_j$ are countably dense

Arbitrary union of measure $0$ open sets has measure $0$ in a separable metric space

If $B$ is a Borel set s.t. $\mu(\partial B)=0$ and $\lim_n\mu_n(B)=\mu(B)$ then does $\lim_n\mu(\overline{B}^{1/n}\setminus\overline{B})=0$ hold?

Calculating a lower bound of Lebesgue measure of some Borel set

A detail on the Polar Coordinate Theorem proof

Borel Measurability of a subset of $R^{\infty}$

regarding measurability of functions

Does a set of positive outer measure contain a measurable set of positive measure?

How can I prove that if $\int_{[0,1]} f~d\nu\leq C\int_{[0,1]} f~d\mu$ then the measures are absolutely continuous?

Borel measure - unbounded sets

proove that $\forall x \in X : \forall \epsilon > 0 : \exists \delta > 0 \text{ s.t. } \mu(B(x,\delta)) ≤ \epsilon$

Is $\mu_U(E) := \mu(E\cap U)$ a Radon measure when $U$ is open?

About the definition of a Borel measurable function in "Measure, Integration & Real Analysis" by Sheldon Axler.

If $f,g$ are two measurable functions on $[0,1]$ such that $\int_A f=\int_A g$ for all $A\subset[0,1]$ such that $\mu(A)=1/3$. Then $f=g$ a.e. $\mu$

Trending Questions

Popular # Hahtags

Popular Questions