(а) Let X %3D {m, п, р, 9}, and 3 {ф, Х, {m}, {n}, {p, 3, {m, п}, {n,p, q}, {m,p, q}Is a sigma algebra over X ?=(b) Define the function m :- [0, 0) byΣ1 if mEА0 if m¢ AHm (A)Prove that 4m:),0, o0) is a measure overΣ

Given: Let X=m, n, p, q and Σ=∅, X, m, n, p, q, m, n, n, p, q, m, p, q. (a) Find whether Σ a sigma…

(a) Let X = {m,n, p, q}, and = {ø, X, {m},{n}, {p, q}, {m,n},{n,p, q}, {m, p, q} %3D a sigma algebra over X ? (b) Define the function m :> → [0, 0) by 1 if mɛ A 0 if m¢ A Hm(A) = { Prove that m :)→ [0, 0) is a measure over Σ

(a) Let X = {m,n, p, q}, and = {ø, X, {m},{n}, {p, q}, {m,n},{n,p, q}, {m, p, q} %3D a sigma algebra over X ? (b) Define the function m :> → [0, 0) by 1 if mɛ A 0 if m¢ A Hm(A) = { Prove that m :)→ [0, 0) is a measure over 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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Question

(а) Let X %3D {m, п, р, 9}, and 3 {ф, Х, {m}, {n}, {p, 3, {m, п}, {n,p, q}, {m,p, q}
Is a sigma algebra over X ?
=
(b) Define the function m :- [0, 0) by
Σ
1 if mEА
0 if m¢ A
Hm (A)
Prove that 4m:),
0, o0) is a measure over
Σ

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