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Writing explicitly the difference of two indicator-like functions (with “non-fixed domain”)
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How can I rewrite explicitly the following difference of indicator functions?
$$int_{0}^A mathbf{1}_{{int_0^x f(s) mathrm{d}s + y + epsilon h> g(x) }}(x,y,z) - mathbf{1}_{{ int_0^x f(s) mathrm{d}s + y > g(x) }}(x,y,z) mathrm{d}x $$
where
$A>0$, $(x,y,z) in mathbb{R}^3$; $f: mathbb{R} to mathbb{R}$, $g:mathbb{R} to mathbb{R}$ are $L^1$ integrable functions, $h in mathbb{R}$ such that $|h| = 1$, and $0 < epsilon ll 1$.
calculus real-analysis functional-analysis sobolev-spaces
asked 23 hours ago
Hiro
102
add a comment |
up vote
-2
down vote
favorite
How can I rewrite explicitly the following difference of indicator functions?
$$int_{0}^A mathbf{1}_{{int_0^x f(s) mathrm{d}s + y + epsilon h> g(x) }}(x,y,z) - mathbf{1}_{{ int_0^x f(s) mathrm{d}s + y > g(x) }}(x,y,z) mathrm{d}x $$
where
$A>0$, $(x,y,z) in mathbb{R}^3$; $f: mathbb{R} to mathbb{R}$, $g:mathbb{R} to mathbb{R}$ are $L^1$ integrable functions, $h in mathbb{R}$ such that $|h| = 1$, and $0 < epsilon ll 1$.
calculus real-analysis functional-analysis sobolev-spaces
asked 23 hours ago
Hiro
102
I don't understand the downvotes.
– Hiro
18 hours ago
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
How can I rewrite explicitly the following difference of indicator functions?
$$int_{0}^A mathbf{1}_{{int_0^x f(s) mathrm{d}s + y + epsilon h> g(x) }}(x,y,z) - mathbf{1}_{{ int_0^x f(s) mathrm{d}s + y > g(x) }}(x,y,z) mathrm{d}x $$
where
$A>0$, $(x,y,z) in mathbb{R}^3$; $f: mathbb{R} to mathbb{R}$, $g:mathbb{R} to mathbb{R}$ are $L^1$ integrable functions, $h in mathbb{R}$ such that $|h| = 1$, and $0 < epsilon ll 1$.
calculus real-analysis functional-analysis sobolev-spaces
asked 23 hours ago
Hiro
102
How can I rewrite explicitly the following difference of indicator functions?
$$int_{0}^A mathbf{1}_{{int_0^x f(s) mathrm{d}s + y + epsilon h> g(x) }}(x,y,z) - mathbf{1}_{{ int_0^x f(s) mathrm{d}s + y > g(x) }}(x,y,z) mathrm{d}x $$
where
$A>0$, $(x,y,z) in mathbb{R}^3$; $f: mathbb{R} to mathbb{R}$, $g:mathbb{R} to mathbb{R}$ are $L^1$ integrable functions, $h in mathbb{R}$ such that $|h| = 1$, and $0 < epsilon ll 1$.
calculus real-analysis functional-analysis sobolev-spaces
calculus real-analysis functional-analysis sobolev-spaces
asked 23 hours ago
Hiro
102
asked 23 hours ago
Hiro
102
edited 22 hours ago
asked 23 hours ago
Hiro
102
asked 23 hours ago
Hiro
102
asked 23 hours ago
Hiro
102
102
I don't understand the downvotes.
– Hiro
18 hours ago
add a comment |
I don't understand the downvotes.
– Hiro
18 hours ago
I don't understand the downvotes.
– Hiro
18 hours ago
I don't understand the downvotes.
– Hiro
18 hours ago
add a comment |
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I don't understand the downvotes.
– Hiro
18 hours ago