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Lectures on Measure Theory and Probability

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Author(s): H.R. Pitt
Publisher: Tata institute of Fundamental Research, Bombay
Year: 1958

Language: English

Measure Theory
Sets and operations on sets
Sequence of sets
Additive system of sets
Set Functions
Continuity of set functions
Extensions and contractions of...
Outer Measure
Classical Lebesgue and Stieltjes measures
Borel sets and Borel measure
Measurable functions
The Lebesgue integral
Absolute Continuity
Convergence theorems
The Riemann Integral
Stieltjes Integrals
L-Spaces
Mappings of measures
Differentiation
Product Measures and Multiple Integrals
Probability
Definitions
Function of a random variable
Parameters of random variables
Joint probabilities and independence
Characteristic Functions
Sequences and limits of...
Examples of characteristic functions
Conditional probabilities
Sequences of Random Variables
The Central Limit Problem
Cumulative sums
Random Functions
Random Sequences and Convergence Properties
Markoff Processes
L2-Processes
Ergodic Properties
Random function with independent increments
Doob Separability and extension theory