diff --git a/coq/ProbTheory/Martingale.v b/coq/ProbTheory/Martingale.v index 767e0ca7..d209eb34 100644 --- a/coq/ProbTheory/Martingale.v +++ b/coq/ProbTheory/Martingale.v @@ -2644,6 +2644,7 @@ Proof. apply Rmax_r. Qed. +(* Lemma double_series_interchange (f : nat -> nat -> R) : (forall n m, 0 <= f n m) -> Series (fun n => Series (fun m => f n m)) = @@ -2677,8 +2678,6 @@ Proof. rewrite <- ex_series_Lim_seq. - Admitted. - Lemma zerotails_eps2k_double_sum_eq (a : nat -> R) (pf:ex_series a) {anneg:NonnegativeFunction a}: Series (fun k => Series (fun x => a (S (x+ (zerotails_eps2k_fun a pf k)%nat)))) = Series (fun n => zerotails_incr_mult a pf n * (a n)). @@ -2722,4 +2721,4 @@ Proof. now rewrite Rmult_comm. Qed. - + *) diff --git a/coq/utils/RbarAdd.v b/coq/utils/RbarAdd.v index 8a58c115..beded618 100644 --- a/coq/utils/RbarAdd.v +++ b/coq/utils/RbarAdd.v @@ -1025,7 +1025,7 @@ Qed. now apply sum_Rbar_n_nneg_nneg. Qed. - +(* (* Fubini for nonnegative reals *) Lemma Series_Series_seq_pair (f:nat->nat->R) : (forall a b, 0 <= (f a b)) -> @@ -1034,7 +1034,7 @@ Qed. Proof. intros. apply Rle_antisym. -Admitted. +*) (* - apply Elim_seq_le_bound; intros. replace (sum_Rbar_n @@ -1331,7 +1331,7 @@ Admitted. - now intros. - now intros. Qed. - +(* Lemma Series_nneg_nested_swap (f:nat->nat->R) : (forall a b, 0 <= (f a b)) -> Series (fun i : nat => Series (fun j : nat => (f i j))) = @@ -1341,7 +1341,7 @@ Admitted. rewrite Series_Series_seq_pair. rewrite Series_Series_seq_pair. - apply Rle_antisym. - + Admitted. +*) (* apply Elim_seq_le_bound; intros. destruct (sum_Rbar_n_iso_swap f n H).