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msc:notes:measure_theory_by_anwar_khan [2021/02/07 16:49] – created - external edit 127.0.0.1msc:notes:measure_theory_by_anwar_khan [2023/05/01 13:36] (current) – removed Administrator
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-====== 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  | 
-^ Provider  |Mr. Anwar Khan  | 
-^ Pages  |169 pages  | 
-^ Format  |PDF (see [[::software]] section for PDF Reader) |  
-^ Size  |7.75 MB  | 
- 
-====Partial contents==== 
-  * 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  
-  * Addition modulo 1  
-  * 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 
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-{{include>msc-notes-viewer.php}} 
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-==== Download or view online ==== 
-<callout type="success" icon="fa fa-download"> 
-  * **{{ :msc:notes:measure-theory-notes-anwar-khan.pdf |Download PDF}}** | VIEW [[:msc:notes:measure theory by anwar khan?f=measure-theory-notes-anwar-khan#online_view|View Online]] 
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-</callout> 
- 
-====Notes of other subjects==== 
-{{topic>msc_notes&simplelist}} 
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-{{tag>MSc MSc_Notes Anwar_Khan}}