[isabelle-dev] NEWS

[Johannes Hölzl]

Session HOL-Probability: Introduced the type "'a measure" to represent
measures, this replaces the records 'a algebra and 'a measure_space. The
locales based on subset_class now have two locale-parameters the space
\<Omega> and the set of measurables sets M. The product of probability spaces
uses now the same constant as the finite product of sigma-finite measure
spaces "PiM :: ('i => 'a) measure". Most constants are defined now
outside of locales and gain an additional parameter, like null_sets,
almost_eventually or \<mu>'. Measure space constructions for distributions
and densities now got their own constants distr and density. Instead of
using locales to describe measure spaces with a finite space, the
measure count_space and point_measure is introduced. INCOMPATIBILITY.

  Renamed constants:
  measure -> emeasure
  finite_measure.\<mu>' -> measure
  product_algebra_generator -> prod_algebra
  product_prob_space.emb -> prod_emb
  product_prob_space.infprod_algebra -> PiM

  Removed locales:
  completeable_measure_space
  finite_measure_space
  finite_prob_space
  finite_product_finite_prob_space
  finite_product_sigma_algebra
  finite_sigma_algebra
  measure_space
  pair_finite_prob_space
  pair_finite_sigma_algebra
  pair_finite_space
  pair_sigma_algebra
  product_sigma_algebra

  Removed constants:
  distribution -> use distr measure, or distributed predicate
  joint_distribution -> use distr measure, or distributed predicate
  product_prob_space.infprod_algebra -> use PiM
  subvimage
  image_space
  conditional_space
  pair_measure_generator

  Replacement theorems:
  sigma_algebra.measurable_sigma -> measurable_measure_of
  measure_space.additive -> emeasure_additive
  measure_space.measure_additive -> plus_emeasure
  measure_space.measure_mono -> emeasure_mono
  measure_space.measure_top -> emeasure_space
  measure_space.measure_compl -> emeasure_compl
  measure_space.measure_Diff -> emeasure_Diff
  measure_space.measure_countable_increasing -> emeasure_countable_increasing
  measure_space.continuity_from_below -> SUP_emeasure_incseq
  measure_space.measure_incseq -> incseq_emeasure
  measure_space.continuity_from_below_Lim -> Lim_emeasure_incseq
  measure_space.measure_decseq -> decseq_emeasure
  measure_space.continuity_from_above -> INF_emeasure_decseq
  measure_space.measure_insert -> emeasure_insert
  measure_space.measure_setsum -> setsum_emeasure
  measure_space.measure_finite_singleton -> emeasure_eq_setsum_singleton
  finite_additivity_sufficient -> ring_of_sets.countably_additiveI_finite
  measure_space.measure_setsum_split -> setsum_emeasure_cover
  measure_space.measure_subadditive -> subadditive
  measure_space.measure_subadditive_finite -> emeasure_subadditive_finite
  measure_space.measure_eq_0 -> emeasure_eq_0
  measure_space.measure_finitely_subadditive -> emeasure_subadditive_finite
  measure_space.measure_countably_subadditive -> emeasure_subadditive_countably
  measure_space.measure_UN_eq_0 -> emeasure_UN_eq_0
  measure_unique_Int_stable -> measure_eqI_generator_eq
  measure_space.measure_Diff_null_set -> emeasure_Diff_null_set
  measure_space.measure_Un_null_set -> emeasure_Un_null_set
  measure_space.almost_everywhere_def -> eventually_ae_filter
  measure_space.almost_everywhere_vimage -> AE_distrD
  measure_space.measure_space_vimage -> emeasure_distr
  measure_space.AE_iff_null_set -> AE_iff_null
  measure_space.real_measure_Union -> measure_Union
  measure_space.real_measure_finite_Union -> measure_finite_Union
  measure_space.real_measure_Diff -> measure_Diff
  measure_space.real_measure_UNION -> measure_UNION
  measure_space.real_measure_subadditive -> measure_subadditive
  measure_space.real_measure_setsum_singleton -> measure_eq_setsum_singleton
  measure_space.real_continuity_from_below -> Lim_measure_incseq
  measure_space.continuity_from_above_Lim -> Lim_emeasure_decseq
  measure_space.real_continuity_from_above -> Lim_measure_decseq
  measure_space.real_measure_countably_subadditive -> measure_subadditive_countably
  finite_measure.finite_measure -> finite_measure.emeasure_finite
  finite_measure.finite_measure_eq -> finite_measure.emeasure_eq_measure
  finite_measure.positive_measure' -> measure_nonneg
  finite_measure.real_measure -> finite_measure.emeasure_real
  finite_measure.empty_measure -> measure_empty
  finite_measure.finite_measure_countably_subadditive -> finite_measure.finite_measure_subadditive_countably
  finite_measure.finite_measure_finite_singleton -> finite_measure.finite_measure_eq_setsum_singleton
  finite_measure.finite_continuity_from_below -> finite_measure.finite_Lim_measure_incseq
  finite_measure.finite_continuity_from_above -> finite_measure.finite_Lim_measure_decseq
  measure_space.simple_integral_vimage -> simple_integral_distr
  measure_space.integrable_vimage -> integrable_distr
  measure_space.positive_integral_translated_density -> positive_integral_density
  measure_space.integral_translated_density -> integral_density
  measure_space.integral_vimage -> integral_distr
  measure_space_density -> emeasure_density
  measure_space.positive_integral_vimage -> positive_integral_distr
  measure_space.simple_function_vimage -> simple_function_comp
  measure_space.simple_integral_vimage -> simple_integral_distr
  pair_sigma_algebra.measurable_cut_fst -> sets_Pair1
  pair_sigma_algebra.measurable_cut_snd -> sets_Pair2
  pair_sigma_algebra.measurable_pair_image_fst -> measurable_Pair1
  pair_sigma_algebra.measurable_pair_image_snd -> measurable_Pair2
  pair_sigma_algebra.measurable_product_swap -> measurable_pair_swap_iff
  pair_sigma_finite.measure_cut_measurable_fst -> pair_sigma_finite.measurable_emeasure_Pair1
  pair_sigma_finite.measure_cut_measurable_snd -> pair_sigma_finite.measurable_emeasure_Pair2
  measure_space.measure_not_negative -> emeasure_not_MInf
  pair_sigma_finite.measure_preserving_swap -> pair_sigma_finite.distr_pair_swap
  pair_sigma_finite.pair_measure_alt -> pair_sigma_finite.emeasure_pair_measure_alt
  pair_sigma_finite.pair_measure_alt2 -> pair_sigma_finite.emeasure_pair_measure_alt2
  pair_sigma_finite.pair_measure_times -> pair_sigma_finite.emeasure_pair_measure_Times
  pair_sigma_algebra.pair_sigma_algebra_measurable -> measurable_pair_swap
  pair_sigma_algebra.pair_sigma_algebra_swap_measurable -> measurable_pair_swap'
  pair_sigma_algebra.sets_swap -> sets_pair_swap
  finite_product_sigma_algebra.in_P -> sets_PiM_I_finite
  Int_stable_product_algebra_generator -> positive_integral
  product_sigma_finite.measure_fold -> product_sigma_finite.distr_merge
  product_sigma_finite.measure_preserving_component_singelton -> product_sigma_finite.distr_singleton
  product_sigma_finite.measure_preserving_merge -> product_sigma_finite.distr_merge
  finite_product_sigma_algebra.P_empty -> space_PiM_empty, sets_PiM_empty
  product_algebra_generator_der -> prod_algebra_eq_finite
  product_algebra_generator_into_space -> prod_algebra_sets_into_space
  product_sigma_algebra.product_algebra_into_space -> space_closed
  product_algebraE -> prod_algebraE_all
  product_algebraI -> sets_PiM_I_finite
  product_measure_exists -> product_sigma_finite.sigma_finite
  sets_product_algebra -> sets_PiM
  sigma_product_algebra_sigma_eq -> sigma_prod_algebra_sigma_eq
  space_product_algebra -> space_PiM
  Int_stable_cuboids -> Int_stable_atLeastAtMost
  measure_space.density_is_absolutely_continuous -> absolutely_continuousI_density
  sigma_finite_measure.RN_deriv_vimage -> sigma_finite_measure.RN_deriv_distr
  prob_space_unique_Int_stable -> measure_eqI_prob_space
  sigma_finite_measure.disjoint_sigma_finite -> sigma_finite_disjoint
  prob_space.measure_space_1 -> prob_space.emeasure_space_1
  prob_space.prob_space_vimage -> prob_space_distr
  prob_space.random_variable_restrict -> measurable_restrict
  measure_preserving -> equality "distr M N f = N" "f : measurable M N"
  measure_unique_Int_stable_vimage -> measure_eqI_generator_eq
  measure_space.measure_preserving_Int_stable -> measure_eqI_generator_eq
  product_prob_space.finite_index_eq_finite_product -> product_prob_space.sets_PiM_generator
  product_prob_space.finite_measure_infprod_emb_Pi -> product_prob_space.measure_PiM_emb
  finite_product_prob_space.finite_measure_times -> finite_product_prob_space.finite_measure_PiM_emb
  product_prob_space.infprod_spec -> product_prob_space.emeasure_PiM_emb_not_empty
  product_prob_space.measurable_component -> measurable_component_singleton
  product_prob_space.measurable_emb -> measurable_prod_emb
  product_prob_space.measurable_into_infprod_algebra -> measurable_PiM_single
  product_prob_space.measurable_singleton_infprod -> measurable_component_singleton
  product_prob_space.measure_emb -> emeasure_prod_emb
  sequence_space.measure_infprod -> sequence_space.measure_PiM_countable
  product_prob_space.measure_preserving_restrict -> product_prob_space.distr_restrict
  prob_space.indep_distribution_eq_measure -> prob_space.indep_vars_iff_distr_eq_PiM
  prob_space.indep_var_distributionD -> prob_space.indep_var_distribution_eq
  conditional_entropy_positive -> conditional_entropy_nonneg_simple
  conditional_entropy_eq -> conditional_entropy_simple_distributed
  conditional_mutual_information_eq_mutual_information -> conditional_mutual_information_eq_mutual_information_simple
  conditional_mutual_information_generic_positive -> conditional_mutual_information_nonneg_simple
  conditional_mutual_information_positive -> conditional_mutual_information_nonneg_simple
  entropy_commute -> entropy_commute_simple
  entropy_eq -> entropy_simple_distributed
  entropy_generic_eq -> entropy_simple_distributed
  entropy_positive -> entropy_nonneg_simple
  entropy_uniform_max -> entropy_uniform
  KL_eq_0 -> KL_same_eq_0
  KL_eq_0_imp -> KL_eq_0_iff_eq
  KL_ge_0 -> KL_nonneg
  mutual_information_eq -> mutual_information_simple_distributed
  mutual_information_positive -> mutual_information_nonneg_simple