-
in file
cantor.v
,- new definitions
cantor_space
,cantor_like
,pointed_discrete
, andtree_of
. - new lemmas
cantor_space_compact
,cantor_space_hausdorff
,cantor_zero_dimensional
,cantor_perfect
,cantor_like_cantor_space
,tree_map_props
,homeomorphism_cantor_like
, andcantor_like_finite_prod
. - new theorem
cantor_surj
.
- new definitions
-
in file
topology.v
,- new lemmas
perfect_set2
, andent_closure
. - lemma
clopen_surj
- new lemmas
-
in
normedtype.v
:- hints for
at_right_proper_filter
andat_left_proper_filter
- hints for
-
in
realfun.v
:- notations
nondecreasing_fun
,nonincreasing_fun
,increasing_fun
,decreasing_fun
- lemmas
cvg_addrl
,cvg_addrr
,cvg_centerr
,cvg_shiftr
,nondecreasing_cvgr
,nonincreasing_at_right_cvgr
,nondecreasing_at_right_cvgr
,nondecreasing_cvge
,nondecreasing_is_cvge
,nondecreasing_at_right_cvge
,nondecreasing_at_right_is_cvge
,nonincreasing_at_right_cvge
,nonincreasing_at_right_is_cvge
- notations
-
in
ereal.v
:- lemmas
ereal_sup_le
,ereal_inf_le
- lemmas
-
in
normedtype.v
:- definition
lower_semicontinuous
- lemma
lower_semicontinuousP
- definition
-
in
numfun.v
:- lemma
patch_indic
- lemma
-
in
lebesgue_measure.v
- lemma
lower_semicontinuous_measurable
- lemma
-
in
lebesgue_integral.v
:- definition
locally_integrable
- lemmas
integrable_locally
,locally_integrableN
,locally_integrableD
,locally_integrableB
- definition
iavg
- lemmas
iavg0
,iavg_ge0
,iavg_restrict
,iavgD
- definitions
HL_maximal
- lemmas
HL_maximal_ge0
,HL_maximalT_ge0
,lower_semicontinuous_HL_maximal
,measurable_HL_maximal
,maximal_inequality
- definition
-
in file
measure.v
- add lemmas
ae_eq_subset
,measure_dominates_ae_eq
.
- add lemmas
-
in
normedtype.v
:- lemmas
vitali_lemma_finite
andvitali_lemma_finite_cover
now returns duplicate-free lists of indices
- lemmas
-
moved from
lebesgue_integral.v
tomeasure.v
:- definition
ae_eq
- lemmas
ae_eq0
,ae_eq_comp
,ae_eq_funeposneg
,ae_eq_refl
,ae_eq_trans
,ae_eq_sub
,ae_eq_mul2r
,ae_eq_mul2l
,ae_eq_mul1l
,ae_eq_abse
- definition
- in
exp.v
:lnX
->lnXn
- in
lebesgue_integral.v
ge0_integral_bigsetU
generalized fromnat
toeqType