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[DRAFT] Some Important Results in Probability Theory
probability
math
Author
Himadri Mandal
Published
March 17, 2025
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Theorem [Lebesgue Differentiation Theorem]
A random variable
\(X\)
has a density
\(f_X\)
iff the CDF
\(F_X\)
is absolutely continous in every closed, bounded interval.
Theorem: Monotone Convergence Theorem
Theorem [Lebesgue Differentiation Theorem]
A random variable
\(X\)
has a density
\(f_X\)
iff the CDF
\(F_X\)
is absolutely continous
1
in every closed, bounded interval.
Proof.
Theorem: Monotone Convergence Theorem
Footnotes
https://en.wikipedia.org/wiki/Absolute_continuity
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