Let X be a set and A be a σ-algebra onX.IS@Suppase AC X. show that the functionf: XR given byf(x)=If X EA/0, If XE ACis A-measurable if and only if A € A.3-9When is a function S: X → RR said to beSimple?© Let x = [0,00), o be the Borel 6-algebraon X and m be the Lebesgue measureon [0). Suppose that f: [0, ∞) Risgiven byf(x) = 20, for all x € [0,D).lim ff. dm = flim fn dm? Justify youranswer.

Introduction: In measure theory, a set A is said to be A-measurable if it belongs to the σ-algebra…

Let X be a Set and X. A be a g-algebra on @Suppose AC X. show that the function f: XR given by flxx) = $-9, If X EA to, if x € AC is A-measurable if and only if A € A. When is a function S:X-R said to be Simple? © Let x = [0, ∞), at be the Borel 6-algebra On X and m be the Lebesgue measure on [0). Suppose that f: [0,00) +R is given by fr (x) = 20, for all x € [0, ∞). lim ff dm = flim fn dm? Justify your 74 answer. IS lim

Let X be a Set and X. A be a g-algebra on @Suppose AC X. show that the function f: XR given by flxx) = $-9, If X EA to, if x € AC is A-measurable if and only if A € A. When is a function S:X-R said to be Simple? © Let x = [0, ∞), at be the Borel 6-algebra On X and m be the Lebesgue measure on [0). Suppose that f: [0,00) +R is given by fr (x) = 20, for all x € [0, ∞). lim ff dm = flim fn dm? Justify your 74 answer. IS lim

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 53EQ

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