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







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  • I don't understand the downvotes.
    – Hiro
    18 hours ago















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







share|cite|improve this question
























  • I don't understand the downvotes.
    – Hiro
    18 hours ago













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







share|cite|improve this question















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






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share|cite|improve this question













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edited 22 hours ago

























asked 23 hours ago









Hiro

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102












  • 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




I don't understand the downvotes.
– Hiro
18 hours ago















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