3.2 Example. Consider the Dirichlet function f: [0, 1] → R defined by if x is rational f(x)= if x is irrational. The function f is clearly bounded and measurable on [0, 1] and hence Lebesgue integrable. Also f(x)=0. However, ƒ is not Riemann inte- 0
3.2 Example. Consider the Dirichlet function f: [0, 1] → R defined by if x is rational f(x)= if x is irrational. The function f is clearly bounded and measurable on [0, 1] and hence Lebesgue integrable. Also f(x)=0. However, ƒ is not Riemann inte- 0
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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![3.2 Example. Consider the Dirichlet function f: [0, 1] R defined
by
1
if x is rational
f(x) =
if x is irrational.
The function f is clearly bounded and measurable on [0, 1] and hence
Lebesgue integrable. Also f(x)=0. However, f is not Riemann inte-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F976eedc2-a972-46ab-947a-700f7b8f127b%2F1a8252f2-80e0-4539-ad38-c198d8aca15b%2Funlhqy5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.2 Example. Consider the Dirichlet function f: [0, 1] R defined
by
1
if x is rational
f(x) =
if x is irrational.
The function f is clearly bounded and measurable on [0, 1] and hence
Lebesgue integrable. Also f(x)=0. However, f is not Riemann inte-
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