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(a) Let X = {m, n, p, q}, and = {ø, X, {m}, {n}, {p, q}, {m, n}, {n, p, q}, {m, p, q}}. Is a sigma algebra over X ? (b) Define the function m :> – [0, 00) by { 1 if m e A 10 if m¢ A Prove that 4m :2→[0, 0) is a measure over (c) Determine 4,m({m, p, q}\{n,p, q}). Hm(A) Σ

(a) Let X = {m, n, p, q}, and = {ø, X, {m}, {n}, {p, q}, {m, n}, {n, p, q}, {m, p, q}}. Is a sigma algebra over X ? (b) Define the function m :> – [0, 00) by { 1 if m e A 10 if m¢ A Prove that 4m :2→[0, 0) is a measure over (c) Determine 4,m({m, p, q}\{n,p, q}). Hm(A) Σ

Advanced Engineering Mathematics
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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(а) Let X %3D {m, п, р.9}, and 3 {ф, х, {m}, {n}, {p, 9}, {m, п}, {n,p, q}, {m, p,9}}. Is > a sigma algebra over X ? (b) Define the function 4m :> – [0, 0) by 1 if mE А 0 if m¢ A Prove that m :)- [0, 00) is a measure over (c) Determine um({m,p, q}\{n,p, q}). Hm (A) = Σ
Transcribed Image Text:(а) Let X %3D {m, п, р.9}, and 3 {ф, х, {m}, {n}, {p, 9}, {m, п}, {n,p, q}, {m, p,9}}. Is > a sigma algebra over X ? (b) Define the function 4m :> – [0, 0) by 1 if mE А 0 if m¢ A Prove that m :)- [0, 00) is a measure over (c) Determine um({m,p, q}\{n,p, q}). Hm (A) = Σ
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