Chapter 01•Analysis & Tactics
The Dirichlet Function & The Birth of Measure Theory
Chapter 02•Analysis & Tactics
The Classical Pathology
Chapter 03•Analysis & Tactics
Failure of the Riemann Integral
Chapter 04•Analysis & Tactics
The Lebesgue Revolution: Partitioning the Co-domain
Practice Quiz•Interactive Assessment
IIT JAM Mathematics • Question Type BExam-Style Practice Problem
Which of the following statements about the Dirichlet function D(x) are TRUE?
A
D(x) is Riemann integrable on [0, 1].
B
D(x) is Lebesgue integrable and ∫₀¹ D dλ = 0.
C
D(x) is discontinuous at every point of ℝ.
D
The set of discontinuities of D(x) has Lebesgue measure 1.
Peer Interaction
Academic Doubts & Colloquium
24 Active Discussions
RS
Ritwik Sen, TIFR CAM2 days ago • Research Scholar
Excellent exposition! The interactive proof canvas in section 2 made the oscillation argument crystal clear. Looking forward to the follow-up article on measure theory applications.