A function : [a, b] ≤ R → R is called a step function if there is a partition a = xo < x₁ < ··· < xn = b of [a, b] and constants ao, a₁, ...., an, b₁, ...., bn E R such that n n $ = Σ akx{xx} + Σ k=0 k=1 Prove that a step function is measurable. bkX (xkxk-1)
A function : [a, b] ≤ R → R is called a step function if there is a partition a = xo < x₁ < ··· < xn = b of [a, b] and constants ao, a₁, ...., an, b₁, ...., bn E R such that n n $ = Σ akx{xx} + Σ k=0 k=1 Prove that a step function is measurable. bkX (xkxk-1)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 51E
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![A function : [a, b] ≤ R → R is called a step function if there is a partition a = x。 < x₁ < ··· < xn = b of
[a, b] and constants a。, a₁, ...., an, b₁,
bn E R such that
n
n
$ = [axX{x} + Σ bxX (xx-²xkK-1)
k=0
k=1
Prove that a step function is measurable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4389b9b9-e475-4746-94da-194021bcd4a6%2F743c429c-81f0-4862-a780-9de4b0801e60%2Fdz6obva_processed.png&w=3840&q=75)
Transcribed Image Text:A function : [a, b] ≤ R → R is called a step function if there is a partition a = x。 < x₁ < ··· < xn = b of
[a, b] and constants a。, a₁, ...., an, b₁,
bn E R such that
n
n
$ = [axX{x} + Σ bxX (xx-²xkK-1)
k=0
k=1
Prove that a step function is measurable.
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