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271 | 271 | section preorder
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272 | 272 | variables [preorder α] [order_closed_topology α] {a b : α}
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273 | 273 |
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274 |
| -lemma is_measurable_Ici : is_measurable (Ici a) := is_closed_Ici.is_measurable |
275 |
| -lemma is_measurable_Iic : is_measurable (Iic a) := is_closed_Iic.is_measurable |
276 |
| -lemma is_measurable_Icc : is_measurable (Icc a b) := is_closed_Icc.is_measurable |
| 274 | +@[simp] lemma is_measurable_Ici : is_measurable (Ici a) := is_closed_Ici.is_measurable |
| 275 | +@[simp] lemma is_measurable_Iic : is_measurable (Iic a) := is_closed_Iic.is_measurable |
| 276 | +@[simp] lemma is_measurable_Icc : is_measurable (Icc a b) := is_closed_Icc.is_measurable |
277 | 277 |
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278 | 278 | instance nhds_within_Ici_is_measurably_generated :
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279 | 279 | (𝓝[Ici b] a).is_measurably_generated :=
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@@ -309,11 +309,15 @@ end partial_order
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309 | 309 | section linear_order
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310 | 310 | variables [linear_order α] [order_closed_topology α] {a b : α}
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311 | 311 |
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312 |
| -lemma is_measurable_Iio : is_measurable (Iio a) := is_open_Iio.is_measurable |
313 |
| -lemma is_measurable_Ioi : is_measurable (Ioi a) := is_open_Ioi.is_measurable |
314 |
| -lemma is_measurable_Ioo : is_measurable (Ioo a b) := is_open_Ioo.is_measurable |
315 |
| -lemma is_measurable_Ioc : is_measurable (Ioc a b) := is_measurable_Ioi.inter is_measurable_Iic |
316 |
| -lemma is_measurable_Ico : is_measurable (Ico a b) := is_measurable_Ici.inter is_measurable_Iio |
| 312 | +@[simp] lemma is_measurable_Iio : is_measurable (Iio a) := is_open_Iio.is_measurable |
| 313 | +@[simp] lemma is_measurable_Ioi : is_measurable (Ioi a) := is_open_Ioi.is_measurable |
| 314 | +@[simp] lemma is_measurable_Ioo : is_measurable (Ioo a b) := is_open_Ioo.is_measurable |
| 315 | + |
| 316 | +@[simp] lemma is_measurable_Ioc : is_measurable (Ioc a b) := |
| 317 | +is_measurable_Ioi.inter is_measurable_Iic |
| 318 | + |
| 319 | +@[simp] lemma is_measurable_Ico : is_measurable (Ico a b) := |
| 320 | +is_measurable_Ici.inter is_measurable_Iio |
317 | 321 |
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318 | 322 | instance nhds_within_Ioi_is_measurably_generated :
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319 | 323 | (𝓝[Ioi b] a).is_measurably_generated :=
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