Theorems · Theorem · number theory
NumberField.mixedEmbedding.convexBodyLT_volume
∀ (K : Type u_1) [inst : Field K] (f : NumberField.InfinitePlace K → NNReal) [inst_1 : NumberField K],
MeasureTheory.volume (NumberField.mixedEmbedding.convexBodyLT K f) =
↑(NumberField.mixedEmbedding.convexBodyLTFactor K) * ↑(∏ w, f w ^ w.mult)The volume of (ConvexBodyLt K f) where convexBodyLT K f is the set of points x
such that ‖x w‖ < f w for all infinite places w.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
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Cites44
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by2
Results whose statement or proof uses this declaration.
- NumberField.Units.dirichletUnitTheorem.seq_nextproof · cited by 3
- NumberField.mixedEmbedding.exists_primitive_element_lt_of_isRealproof · cited by 1