(a) Let ) be a o- Algebra on X. Assume that 41; µ2:)→ [0, ) are two measures on X. Is 41 + kuz 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(AUB) = µ(A) + µ(B) – µ(An B). %3D

(a) Let ) be a o- Algebra on X. Assume that 41; µ2:)→ [0, ) are two measures on X. Is 41 + kuz 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(AUB) = µ(A) + µ(B) – µ(An B). %3D

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

(a) Let > be a o- Algebra on X.
Assume that 41; H2 : → [0, ∞) are two measures on X.
Is µ1 + kuz 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(AUB) = µ(A) + µ(B) – µ(An B).
%3D

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