Theorems · Theorem · probability
ProbabilityTheory.map_cast_binomial_real_zero
∀ {R : Type u_1} [inst : MeasurableSpace R] [inst_1 : AddMonoidWithOne R] [MeasurableSingletonClass R] [CharZero R]
(n : ℕ) (p : ↑unitInterval),
(MeasureTheory.Measure.map Nat.cast (ProbabilityTheory.binomial n p)).real {0} = (1 - ↑p) ^ n- Cited by
- 0 results in Mathlib
- Foundations
- Depth 292 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- Set.Elemstatement and proof · cited by 7,166
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- pow_zeroproof · cited by 1,094
- CharZerostatement and proof · cited by 932
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- unitIntervalstatement and proof · cited by 607
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