Question

(2) Give an example of an algebra A in P(N) which is not a $\sigma$-algebra, and an example of a function $\rho$: A $\to$ [0, 1], such that $\rho(\emptyset)$ = 0, and $\rho(N)$ = 1, for which the outer measure $\rho^*$ is identically equal to zero.

Name: 2 give an example of an algebra a in pn which is not a sigma algebra and an example of a function rho a to 0 1 such that rhoemptyset 0 and rhon 1 for which the outer measure rho is identical 04076
Uploaded: 2023-10-11T11:58:39-08:00
Duration: 2 min 58 s
Channel: Supreeta N
Description: 2 give an example of an algebra a in pn which is not a sigma algebra and an example of a function rho a to 0 1 such that rhoemptyset 0 and rhon 1 for which the outer measure rho is identical 04076

          (2) Give an example of an algebra A in P(N) which is not a $\sigma$-algebra, and an example of a function $\rho$: A $\to$ [0, 1], such that $\rho(\emptyset)$ = 0, and $\rho(N)$ = 1, for which the outer measure $\rho^*$ is identically equal to zero.

2 give an example of an algebra a in pn which is not a sigma algebra and an example of a function rho a to 0 1 such that rhoemptyset 0 and rhon 1 for which the outer measure rho is identical 04076

Added by Brian A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

10/11/2023

Step 1

This is not a $\sigma$-algebra because it does not contain the countable union of disjoint sets. For example, consider the sets $A_i = \{i\}$ for $i \in N$. Each $A_i$ is in A, but $\bigcup_{i=1}^\infty A_i = N$, which is in A, but the union of infinitely many Show more…

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(2) Give an example of an algebra A in P(N) which is not a $\sigma$-algebra, and an example of a function $\rho$: A $\to$ [0, 1], such that $\rho(\emptyset)$ = 0, and $\rho(N)$ = 1, for which the outer measure $\rho^*$ is identically equal to zero.