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Changelog (unreleased)

[Unreleased]

Added

  • in set_interval.v:

    • lemmas setU_itvob1, setU_1itvob

  • in realfun.v:

    • lemma derivable_sqrt

  • in classical_sets.v:

    • definition rectangle
    • lemmas rectangle_setX, setI_closed_rectangle
    • definitions cross, cross12
    • lemmas smallest_sub_sub, bigcap_closed_smallest, smallest_sub_iff
    • lemma preimage_set_systemS

  • in measurable_structure.v:

    • lemmas g_sigma_algebra_cross, g_sigma_algebra_rectangle

  • in measurable_function.v:

    • lemma preimage_measurability

  • in pseudometric_normed_Zmodule.v:

    • lemma itv_center_shift

  • in normed_module.v:

    • lemmas closure_itvoo

  • in unstable.v:

    • structures SemiNorm, Norm
    • lemmas normMn, normN, ler_norm_sum

  • in normed_module.v:

    • structure NormedVector
    • notation normedVectType
    • definition max_space
    • lemmas sup_closed_ball_compact, equivalence_norms, linear_findim_continuous

  • in tvs.v:

    • lemmas cvg_sum, sum_continuous

  • in classical_sets.v:

    • lemmas setI_closed_setT, setI_closed_set0

  • in measurable_function.v:

    • lemma g_sigma_algebra_preimage_comp

  • in measure_function.v:

    • lemma g_sigma_algebra_finite_measure_unique

  • new file independence.v:

    • definition independent_events
    • definition mutual_independence
    • lemma eq_mutual_independence
    • definition independence2, independence2P
    • lemma mutual_independence_fset
    • lemma mutual_independence_finiteS
    • theorem mutual_independence_finite_g_sigma
    • lemma mutual_dependence_bigcup
    • definition independent_RVs
    • lemma independent_RVsD1
    • theorem independent_generators
    • definition independent_RVs2
    • lemmas independent_RVs2_comp, independent_RVs2_funrposneg, independent_RVs2_funrnegpos, independent_RVs2_funrnegneg, independent_RVs2_funrpospos
    • definition pairRV, lemma measurable_pairRV
    • lemmas independent_RVs2_product_measure1
    • lemmas independent_RVs2_setI_preimage, independent_Lfun1_expectation_product_measure_lty
    • lemma ge0_independent_expectationM
    • lemmas independent_Lfun1_expectationM_lty, independent_Lfun1M, independent_expectationM

  • in ereal.v:

    • lemma ge0_addBefctE

  • in measure_extension.v:

    • definition caratheodory_measure

  • in measurable_structure.v:

    • structure PMeasurable, notation pmeasurableType

  • in subspace_topology.v:

    • lemma withinU_continuous_patch

  • in matrix_normedtype.v:

    • lemma continuous_mx

  • in derive.v:

    • instance is_derive_mx
    • fact dmx
    • lemma diffmx
    • lemma is_diff_mx
    • instance is_diff_mx

  • in functions.v:

    • lemmas linfunP, linfun_eqP
    • instances of SubLmodule and pointedType on {linear _->_ | _ }

  • in tvs.v:

    • structure LinearContinuous
    • factory isLinearContinuous
    • instance of ChoiceType on {linear_continuous _ -> _ }
    • instance of LinearContinuous with the composition of two functions of type LinearContinuous
    • instance of LinearContinuous with the sum of two functions of type LinearContinuous
    • instance of LinearContinuous with the scalar multiplication of a function of type LinearContinuous
    • instance of Continuous on -f when f is of type LinearContinuous
    • instance of SubModClosed on {linear_continuous _ -> _}
    • instance of SubLModule on {linear_continuous _ -> _ }
    • instance of LinearContinuous on the null function
    • notations {linear_continuous _ -> _ | _ } and {linear_continuous _ -> _ }
    • definitions lcfun, lcfun_key, lcfunP
    • lemmas lcfun_eqP, null_fun_continuous, fun_cvgD, fun_cvgN, fun_cvgZ, fun_cvgZr
    • lemmas lcfun_continuous and lcfun_linear

  • new files signed_measure.v and radon_nikodym.v

    • with the contents of charge.v (deprecated)

Changed

  • moved from measurable_structure.v to classical_sets.v:

    • definition preimage_set_system
    • lemmas preimage_set_system0, preimage_set_systemU, preimage_set_system_comp, preimage_set_system_id

  • moved from measurable_structure.v to classical_sets.v:

    • definition preimage_set_system
    • lemmas preimage_set_system0, preimage_set_systemU, preimage_set_system_comp, preimage_set_system_id

  • moved from topology_structure.v to filter.v:

    • lemma continuous_comp (and generalized)

  • in numfun.v:

    • fune_abse renamed to funeposDneg and direction of the equality changed
    • funeposneg renamed to funeposBneg and direction of the equality changed
    • funeD_posD renamed to funeDB and direction of the equality changed

  • in constructive_ereal.v:

    • lemmas EFin_semi_additive and dEFin_semi_additive turned into Lets

  • moved from charge.v to signed_measure.v:

    • mixin isAdditiveCharge, structure AdditiveCharge
    • mixin isSemiSigmaAdditive, structure Charge
    • factory isCharge
    • lemmas charge0, charge_semi_additiveW, charge_semi_additive2E, charge_semi_additive2, chargeU, chargeDI, charge_partition
    • definitions measure_of_charge, charge_of_finite_measure
    • lemma chargeD
    • definitions crestr, crestr0, czero, cscale
    • lemmas dominates_cscalel, dominates_cscaler
    • definition copp
    • lemma cscaleN1
    • definition cadd
    • lemmas dominates_cadd, dominates_pushforward
    • definitions positive_set, negative_set
    • lemmas negative_set_charge_le0, negative_set0, positive_negative0, bigcup_negative_set, negative_setU, hahn_decomposition_lemma
    • definition hahn_decomposition
    • theorem Hahn_decomposition
    • lemmas Hahn_decomposition_uniq, cjordan_posE, cjordan_negE
    • definitions jordan_pos, jordan_neg
    • lemmas jordan_posE, jordan_negE, jordan_decomp, jordan_pos_dominates, jordan_neg_dominates
    • definition charge_variation, charge_dominates
    • lemmas abse_charge_variation, null_charge_dominatesP, content_charge_dominatesP, charge_variation_continuous

  • moved from charge.v to radon_nikodym.v:

    • definition induced_charge
    • lemmas semi_sigma_additive_nng_induced, dominates_induced, integral_normr_continuous
    • definitions approxRN, int_approxRN, sup_int_approxRN
    • lemmas sup_int_approxRN_ge0, radon_nikodym_finite, radon_nikodym_sigma_finite, change_of_variables, integrableM, chain_rule
    • definition Radon_Nikodym
    • lemmas Radon_NikodymE, Radon_Nikodym_fin_num, Radon_Nikodym_integrable, ae_eq_Radon_Nikodym_SigmaFinite, Radon_Nikodym_change_of_variables, Radon_Nikodym_cscale, Radon_Nikodym_cadd, Radon_Nikodym_chain_rule

Renamed

  • in tvs.v:

    • definition tvsType -> convexTvsType
    • class Tvs -> ConvexTvs
    • mixin Uniform_isTvs -> Uniform_isConvexTvs
    • factory PreTopologicalLmod_isTvs -> PreTopologicalLmod_isConvexTvs
    • section Tvs_numDomain -> ConvexTvs_numDomain
    • section Tvs_numField -> ConvexTvs_numField
    • section prod_Tvs -> prod_ConvexTvs

  • in normed_module.v

    • mixin PseudoMetricNormedZmod_Tvs_isNormedModule -> PseudoMetricNormedZmod_ConvexTvs_isNormedModule

  • in measurable_structure.v:

    • measurable_prod_measurableType -> prod_measurable_rectangle

  • in measurable_realfun.v:

    • measurable_fun_itv_co -> measurable_fun_itvbb_itvco
    • measurable_fun_itv_oc -> measurable_fun_itvbb_itvoc
    • emeasurable_fun_itv_cc -> emeasurable_fun_itvbb_itvcc
    • measurable_fun_itv_cc -> measurable_fun_itvbb_itvcc
    • measurable_fun_itv_bndo_bndcP -> measurable_fun_itvbo_itvbcP
    • emeasurable_fun_itv_bndo_bndcP -> emeasurable_fun_itvbo_itvbcP
    • measurable_fun_itv_obnd_cbndP -> measurable_fun_itvob_itvcbP
    • emeasurable_fun_itv_obnd_cbndP -> emeasurable_fun_itvob_itvcbP

  • in lebesgue_integral_nonneg.v:

    • integral_itv_bndo_bndc -> integral_itvbo_itvbc
    • integral_itv_obnd_cbnd -> integral_itvob_itvcb
    • integral_itv_bndoo -> integral_itvbb_itvoo

  • in lebesgue_Rintegral.v:

    • Rintegral_itv_bndo_bndc -> Rintegral_itvbo_itvbc
    • Rintegral_itv_obnd_cbnd -> Rintegral_itvob_itvcb

  • in topology_structure.v:

    • cts_fun -> continuous_fun

  • in measure_function.v:

    • isFinite -> isFinNumFun

Generalized

  • in measurable_structure.v:

    • lemma sigma_algebra_measurable (not specialized to setT anymore)

  • in measurable_function.v:

    • lemma preimage_set_system_measurable_fun

  • in measurable_structure.v

    • structure SemiRingOfSets, mixin isSigmaRing, factories isRingOfSets, isRingOfSets_setY, isAlgebraOfSets, isAlgebraOfSets_setD, isMeasurable are not required to be pointed anymore
    • lemmas measurable_g_measurableTypeE, g_sigma_algebra_preimageType, g_sigma_algebra_preimage, g_sigma_preimageE, g_sigma_preimageE, g_sigma_algebra_rectangle are generalized from pointedType to choiceType (the list might not be exhaustive)

  • in ereal.v:

    • lemma funID generalized from pointedType to Type

  • in numfun.v:

    • lemma indic_restrict generalized from pointedType to Type
    • factory FiniteDecomp generalized from pointedType/nzRingType to Type/pzRingType

  • in simple_functions.v:

    • lemmas fctD, fctN, fctM, fctZ

Deprecated

  • file charge.v (use measure.v and/or lebesgue_integral.v)

Removed

  • file signed.v

  • in measurable_structure.v:

    • lemmas measurable_prod_g_measurableType, measurable_prod_g_measurableTypeR

Infrastructure

Misc