# Advance Analysis by Ms. Iqra Liaqat

These notes are send by Ms. iqra-liaqat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org

Name | Advance Analysis |
---|---|

Sender | Ms. Iqra Liaqat |

Author | Unknown |

Pages | 222 pages |

Format | PDF (see Software section for PDF Reader) |

Size | 7.92 mB |

### Contents & Summary

In this section, the main heading of the definitions are given below.

- Rational numbers
- Proper subset
- Function
- One-one function, onto function
- Equivalence set
- Infinite set
- Denumerable set
- Countable set
- Uncountable set
- Choice functions
- Cardinal number
- Finite cardinal number
- Exponent of cardinals
- Schroeder Bernstein theorem
- Continum hypothesis
- Cantor's theorem
- Set theory
- Partially and totally ordered set
- Similar sets
- Well ordered set
- Ordinal numbers
- Axiom of choice
- Zorn's lemma

- Well ordered sets and ordinal numbers
- Principle of transfinite induction
- Limit elements
- Multiplication of ordinals
- Zorn's lemma
- Choice functions
- Set function
- Finitely additive set function
- Pre-measure
- Outer measure
- Monotone set function
- Sum of two outer measure
- Scalar multiplication of an outer measure
- Difference of two outer measure
- Lebesgue outer measure
- $\sigma$-Algebra
- Borel field
- Lebesgue measure
- Measurable function
- Characteristics functions
- Simple function
- Riemann integration
- Monotone convergence theorem
- Convergence in measure

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- Last modified: 6 weeks ago
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