Q3.(a) Let X = {m, n, P, q}, and = {¢, X, {m}, {n}, {p, q}, {m,n}, {n,p, q}, {m, p, g}}.Is > a sigma algebra over X ?(b) Define the function um :> – [0, 0) by1 if m e A0 if m¢ AProve that um :)→ [0, 0) is a measure over(c) Determine ,m({m, p, q}\{n, P, q}).Hm (A)Σ

Name: Q3.(a) Let X = {m, n, P, q}, and = {¢, X, {m}, {n}, {p, q}, {m,n}, {n
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Description: Q3.(a) Let X = {m, n, P, q}, and = {¢, X, {m}, {n}, {p, q}, {m,n}, {n,p, q}, {m, p, g}}.Is > a sigma algebra over X ?(b) Define the function um :> – [0, 0) by1 if m e A0 if m¢ AProve that um :)→ [0, 0) is a measure over(c) Determine ,m({m, p, q}\{n,

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Q3. (a) Let X = {m, n, P, q}, and = {0, X, {m}, {n}, {p, q}, {m, n}, {n,p, q}, {m, p, q}}. Is > a sigma algebra over X ? (b) Define the function Hm :> – [0, 0) by 1 if m e A 0 if m¢ A Hm(A) = Prove that um :)→ [0, 00) is a measure over (c) Determine 4m({m,p,q}\{n,p, q}). Σ

Q3. (a) Let X = {m, n, P, q}, and = {0, X, {m}, {n}, {p, q}, {m, n}, {n,p, q}, {m, p, q}}. Is > a sigma algebra over X ? (b) Define the function Hm :> – [0, 0) by 1 if m e A 0 if m¢ A Hm(A) = Prove that um :)→ [0, 00) is a measure over (c) Determine 4m({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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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Q3.
(a) Let X = {m, n, P, q}, and = {¢, X, {m}, {n}, {p, q}, {m,n}, {n,p, q}, {m, p, g}}.
Is > a sigma algebra over X ?
(b) Define the function um :> – [0, 0) by
1 if m e A
0 if m¢ A
Prove that um :)→ [0, 0) is a measure over
(c) Determine ,m({m, p, q}\{n, P, q}).
Hm (A)
Σ

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