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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-dde | Structured version Visualization version GIF version |
Description: Define the Dirac delta measure. (Contributed by Thierry Arnoux, 14-Sep-2018.) |
Ref | Expression |
---|---|
df-dde | ⊢ δ = (𝑎 ∈ 𝒫 ℝ ↦ if(0 ∈ 𝑎, 1, 0)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdde 31912 | . 2 class δ | |
2 | va | . . 3 setvar 𝑎 | |
3 | cr 10728 | . . . 4 class ℝ | |
4 | 3 | cpw 4513 | . . 3 class 𝒫 ℝ |
5 | cc0 10729 | . . . . 5 class 0 | |
6 | 2 | cv 1542 | . . . . 5 class 𝑎 |
7 | 5, 6 | wcel 2110 | . . . 4 wff 0 ∈ 𝑎 |
8 | c1 10730 | . . . 4 class 1 | |
9 | 7, 8, 5 | cif 4439 | . . 3 class if(0 ∈ 𝑎, 1, 0) |
10 | 2, 4, 9 | cmpt 5135 | . 2 class (𝑎 ∈ 𝒫 ℝ ↦ if(0 ∈ 𝑎, 1, 0)) |
11 | 1, 10 | wceq 1543 | 1 wff δ = (𝑎 ∈ 𝒫 ℝ ↦ if(0 ∈ 𝑎, 1, 0)) |
Colors of variables: wff setvar class |
This definition is referenced by: ddeval1 31914 ddeval0 31915 ddemeas 31916 |
Copyright terms: Public domain | W3C validator |