Proving: Consider the decreasing sequence of functions {f„} defined on R, where fn(x) = X[n,00), Vn e N.That is, f, is the characteristic function of the interval [n, 0) for all n e N.Let f = 0 on R or f(r) = 0 for any r e R. Show that fn+ f pointwise on R, that is, lim fn(r) = 0, Vr e R.%3D

The given function is fnx=ℵ[n, ∞) for every n∈ℕ, where fn is the characteristic function of the…

Answered: Consider the decreasing sequence of…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Consider the decreasing sequence of functions {f„} defined on R, where fn(x) = X[n,00), Vn e N. That is, fn is the characteristic function of the interval [n, 0) for all n ɛ N. Let ƒ = 0 on R or f(r) = 0 for any re R. Show that fn + f pointwise on R, that is, lim fn(r) = 0, Vr E R.