[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ6 (1002ﾚｽ)
上下前次1-新
抽出解除 ﾚｽ栞

---

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索 歴削→次ｽﾚ 栞削→次ｽﾚ 過去ﾛｸﾞﾒﾆｭｰ

---

268(2): 2024/01/29(月)07:58 ID:2Tor3z84(3/4) AAS
つづき

We now show that for every ε > 0, there are upper and lower sums whose difference is less than ε, from which Riemann integrability follows. To this end, we construct a partition of [a, b] as follows:

Denote ε1 = ε / 2(b − a) and ε2 = ε / 2(M − m), where m and M are the infimum and supremum of f on [a, b]. Since we may choose intervals {I(ε1)i} with arbitrarily small total length, we choose them to have total length smaller than ε2.

Each of the intervals {J(ε1)i} has an empty intersection with Xε1, so each point in it has a neighborhood with oscillation smaller than ε1. These neighborhoods consist of an open cover of the interval, and since the interval is compact there is a finite subcover of them. This subcover is a finite collection of open intervals, which are subintervals of J(ε1)i (except for those that include an edge point, for which we only take their intersection with J(ε1)i). We take the edge points of the subintervals for all J(ε1)i − s, including the edge points of the intervals themselves, as our partition.

Thus the partition divides [a, b] to two kinds of intervals:
省7

---

270(1): 2024/01/29(月)09:37 ID:2GVFwqXV(1/2) AAS
>>266-269　それ日本で要約して書いてみ

---

271(4): 2024/01/29(月)10:41 ID:F9Ii6wqO(1) AAS
>>270
>>>266-269　それ日本で要約して書いてみ

面白い漫才師だな
するりとうまく「体を入れ替える」話法ねｗ

下記は、君が”大学数学ゼミ、かくあるべし”！>>262
と主張していたことだよ

で、そのしたり顔の主張をつぶしに行ったのが、私です
省27

---

上下前次1-新書関写板覧索設栞歴

---

ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ

---

ぬこの手 ぬこTOP 0.034s