# Measure Theory Notes by Anwar Khan

Handwritten notes of measure theory by [[people:anwar-khan]]. These notes are good to cover measure theory paper at master level. We are very thankful to [[people:anwar-khan]] for sending these notes.

 Name Measure Theory: Notes Mr. Anwar Khan 169 pages PDF (see Software section for PDF Reader) 7.75 MB
• Algebra on $X$
• Sigma Algebra i.e. $\sigma-$algebra on $X$
• Trivial $\sigma-$algebra; Largest $\sigma-$algebra
• Increasin & sequence of sets
• Decreasing sequence of sets
• Define $\lim\limits_{k\to \infty} \sup A_k$ and $\lim\limits_{k\to \infty} \inf A_k$
• Smallest $\sigma-$algebra
• Borel set & Borel $\sigma-$algebra
• $G_\sigma-$set; $F_\sigma-$set
• Set of extended real numbers; Set function; Properties of set function
• Measure
• Finite measure; $\sigma-$finite measure
• Monotone convergence theorem
• Measurable space and measure space; Finite measure space; $\sigma-$finite measure space; $\mathcal{A}-$measurable set
• $\sigma-$finite set
• Null set
• Complete $\sigma-$algebra; Complete
• measure space; Outer measure
• $\mu^*-$measurable set
• Lebesgue outer measure
• Lebesgue measurable set or $\mu^*-$measurable set; Lebesgue $\sigma-$algebra; Lebesgue measurable space
• Lebesgue measure space
• Dense sub set of $X$
• Translation of a set; Dielation of a set
• Translation invarient
• Translation of $E$ mod 1
• Measurable function
• Characteristic function
• Almost every where property; Equal almost every where
• Limit inferior and limit superior of real value sequence
• Sequence of $\mathcal{A}-$measurable functions & its limits & their properties
• Larger & smaller of two function; Positive part of $f$; Negative part of $f$; Absolute function of $f$
• Limit existence almost every where
• Step function
• Riemann integral
• Simple function; Canonical representation of simple function
• Lebesgue integral of simple function
• Bounded function; Lower Lebesgue integral; Upper Lebesgue integral
• Lebesgue integral of bounded function
• Uniform convergence
• Almost uniform convergence; Egoroff's theorem; Bounded convergence theorem; Non-negative function; Lebesgue integralof non-negative function
• Monotone convergence theorem
• Fatou's lemma

Please click on View Online to see inside the PDF.

• msc/notes/measure_theory_by_anwar_khan