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msc:notes:measure_theory_by_anwar_khan [2021/02/07 16:49] – created - external edit 127.0.0.1 | msc: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: | ||
- | ^ Name |Measure Theory: Notes | | ||
- | ^ Provider | ||
- | ^ Pages |169 pages | | ||
- | ^ Format | ||
- | ^ Size |7.75 MB | | ||
- | |||
- | ====Partial contents==== | ||
- | * Algebra on $X$ | ||
- | * Sigma Algebra i.e. $\sigma-$algebra on $X$ | ||
- | * Trivial $\sigma-$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; | ||
- | * 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; | ||
- | * measure space; Outer measure | ||
- | * $\mu^*-$measurable set | ||
- | * Lebesgue outer measure | ||
- | * Lebesgue measurable set or $\mu^*-$measurable set; Lebesgue $\sigma-$algebra; | ||
- | * 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; | ||
- | * Monotone convergence theorem | ||
- | * Fatou' | ||
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- | {{include> | ||
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- | ==== Download or view online ==== | ||
- | <callout type=" | ||
- | * **{{ : | ||
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- | </ | ||
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- | ====Notes of other subjects==== | ||
- | {{topic> | ||
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