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%------------------------------------------------------------------------------
% Top file for measure_integration_fnd
%
% Author: David Lester, Manchester University, NIA, Université Perpignan
%
% All references are to SK Berberian "Fundamentals of Real Analysis",
% Springer, 1991
%
% Version 1.0 1/5/07 Initial Version
%------------------------------------------------------------------------------
top: THEORY
BEGIN
IMPORTING
% Local Extras
partitions, % Partitioning a set into a setofsets
pointwise_convergence, % Pointwise functional convergence
sup_norm, % sup_norm(f) = sup(abs(f))
product_sections, % sections of sets [T1,T2]
% Borel sets and functions
subset_algebra_def, % Definitions of Sigma/Subset Algebras
subset_algebra, % Properties of Subset Algebras
sigma_algebra, % Properties of Sigma Algebras
product_sigma_def, % Product sigma-algebra definition
product_sigma, % product sigma-algebras properties
borel, % Borel sets
hausdorff_borel, % In Hausdorff Space singletons are Borel
borel_functions, % Borel Functions
identity_borel, % ... preserved by identity and ...
composition_borel, % ... and composition
real_borel, % Borel sets of the reals
% Measures
generalized_measure_def, % Measures over setofsets containing emptyset
measure_def, % Measures over a _subset_ algebra
measure_space_def, % Measurable sets and functions on a sigma-algebra
measure_space, % Simple functions and their limits
outer_measure_def, % Outer measure definition
ast_def, % Generalized Measure-induced outer measures
outer_measure, % ... as above on subset algebras
outer_measure_props, % outer measure properties
measure_props, % measure properties
measure_theory, % negligible/null definitions; also ae properties
monotone_classes, % Monotone Class Lemma
hahn_kolmogorov, % Hahn-Kolmogorov extension theorem
% Finite Measures
finite_measure,
% Extras for complete measures
complete_measure_theory, % Extras for complete measures
measure_completion_aux, % The gory details for ...
measure_completion, % Completing the measure, by making all
% negligible sets null
% Integration
isf, % integrable simple functions
nn_integral, % integrals of functions [T->nnreal]
integral, % integrals of functions [T->real]
finite_integral, % integrals over finite measures
integral_convergence_scaf, % Preliminary for Monotone Convergence theorem
integral_convergence, % Monotone and dominated convergence theorems
complete_integral, % Simplified form of above for complete measures
indefinite_integral, % Indefinite integrals
measure_equality, % Integrals on equal measures
measure_contraction, % Measures on subsets of T ...
measure_contraction_props, % ... and integrability
sigma_finite_measure_props, % specialization for sigma-finite measures
% Products
product_finite_measure, % Products of finite measures
product_measure, % Products of sigma-finite measures
% Product Integrals
product_integral_def, % Product integral defs
finite_fubini_scaf, % Fubini-Tonelli Lemmas for finite measures and
% integrable simple functions
finite_fubini_tonelli, % Fubini-Tonelli Lemmas for finite measures
finite_fubini, % Fubini's Theorem for finite measures
fubini_tonelli_scaf, % Preparatory results for ...
fubini_tonelli, % Fubini-Tonelli Lemmas for sigma-finite measures
fubini % Fubini's Theorem for sigma-finite measures
END top
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