Q3.(a) Let X = {m, n,p,q}, andE= {6, X, {m}, {n}, {p, q}, {m, n}, {n,p, q}, {m, p, q}}.Is a sigma algebra over X ?- (0, 0) by1 if me A0 if m¢ AProve that Hm :)→ [0, 0) is a measure over(c) Determine 4m({m,p,q}\{n,p, q}).(b) Define the function 4mHm(A) = •Σ

Answered: Image /qna-images/answer/b46ef8bd-4a0c-4be4-b0e4-efc816db61d7.jpg

Q3. (a) Let X = {m,n, p,9}, and = {ó, X, {m}, {n}, {p.q}, {m, n}, {n,p, q}, {m, p, q}}. Is a sigma algebra over X ? (b) Define the function m :E- (0, 0) by %3D | Hm(A) = {1 if mɛ A 0 if m¢ A Prove that m :> →[0, 0) is a measure over (c) Determine H„({m,p.q}\{n,p,q}). Σ

Q3. (a) Let X = {m,n, p,9}, and = {ó, X, {m}, {n}, {p.q}, {m, n}, {n,p, q}, {m, p, q}}. Is a sigma algebra over X ? (b) Define the function m :E- (0, 0) by %3D | Hm(A) = {1 if mɛ A 0 if m¢ A Prove that m :> →[0, 0) is a measure over (c) Determine H„({m,p.q}\{n,p,q}). Σ

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q3.
(a) Let X = {m, n,p,q}, and
E= {6, X, {m}, {n}, {p, q}, {m, n}, {n,p, q}, {m, p, q}}.
Is a sigma algebra over X ?
- (0, 0) by
1 if me A
0 if m¢ A
Prove that Hm :)→ [0, 0) is a measure over
(c) Determine 4m({m,p,q}\{n,p, q}).
(b) Define the function 4m
Hm(A) = •
Σ

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