[分析] Rudin實變課本32頁的第5題(b)

[Rudin5566 (魯丁.嗚嗚溜溜)]

Prove that the set of points at which a sequence of measurable real-valued fun-

ctions converges(to a finite limit) is measurable.

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◆ From: 140.122.140.165
→ THEJOY      :只要會證明，可測函數構成的序列，其limsup和liminf
→ THEJOY      :也可測即可
→ willydp     :εδcriterion + {measurable sets} is a σ-algebra
→ Rudin5566   :為什麼只要證limsup和liminf也可測就好呢？
推 c76068      :因為收斂的點的集合 就是{x:limsup f = liminf f}
→ c76068      :現在limsup f 和liminf f都是可測函數
→ c76068      :{x:limsup 不等於 liminf}就是可測的