Q4. (a) Let > be a o- Algebra on X. Assume that u1, µ2 : ) → [0, ∞) are two measures on X. Is 41 + kµ2 a measure on X? where k is a scalar. Consider the cases: k 20 and k < 0. (b) Let (X, , 4) be a measure space. For A, BE ). Show that u(AUB) = µ(A) + µ(B) – µ(An B). -

Q4. (a) Let > be a o- Algebra on X. Assume that u1, µ2 : ) → [0, ∞) are two measures on X. Is 41 + kµ2 a measure on X? where k is a scalar. Consider the cases: k 20 and k < 0. (b) Let (X, , 4) be a measure space. For A, BE ). Show that u(AUB) = µ(A) + µ(B) – µ(An B). -

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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Q4.
(a) Let > be a o-
Algebra on X.
Assume that 41, #2 :) → [0, ∞) are two measures on X.
Is µ1 + kµ2 a measure on X? where k is a scalar.
Consider the cases: k >0 and k < 0.
(b) Let (X, ), µ) be a measure space. For A, Be ).
Show that u(AU B) = µ(A) + µ(B) – µ(An B).

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