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Let f(x,y),0≤x,y≤1, satisfy the following conditions: for each x,f(x,y) is an integrable function of y, and (∂f(x,y)/∂x) is a bounded function of (x,y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and dx d ∫ 0 1 f(x,y)dy=∫ 0 1 ∂x ∂ f(x,y)dy

Home/ Let f(x,y),0≤x,y≤1, satisfy the following conditions: for each x,f(x,y) is an integrable function of y, and (∂f(x,y)/∂x) is a bounded function of (x,y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and dx d ∫ 0 1 f(x,y)dy=∫ 0 1 ∂x ∂ f(x,y)dy

Let f(x,y),0≤x,y≤1, satisfy the following conditions: for each x,f(x,y) is an integrable function of y, and (∂f(x,y)/∂x) is a bounded function of (x,y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and dx d ∫ 0 1 f(x,y)dy=∫ 0 1 ∂x ∂ f(x,y)dy

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Let f(x,y),0≤x,y≤1, satisfy the following conditions: for each x,f(x,y) is an integrable function of y, and (∂f(x,y)/∂x) is a bounded function of (x,y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and dx d ∫ 0 1 f(x,y)dy=∫ 0 1 ∂x ∂ f(x,y)dy

chun 9 months 2024-12-22T11:21:26+05:00 2024-12-22T11:21:26+05:00 0 Answers 4 views Beginner

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Let f(x,y),0≤x,y≤1, satisfy the following conditions: for each x,f(x,y) is an integrable function of y, and (∂f(x,y)/∂x) is a bounded function of (x,y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and dx d ​ ∫ 0 1 ​ f(x,y)dy=∫ 0 1 ​ ∂x ∂ ​ f(x,y)dy

Let f(x,y),0≤x,y≤1, satisfy the following conditions: for each x,f(x,y) is an integrable function of y, and (∂f(x,y)/∂x) is a bounded function of (x,y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and dx d ​ ∫ 0 1 ​ f(x,y)dy=∫ 0 1 ​ ∂x ∂ ​ f(x,y)dy

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Let f(x,y),0≤x,y≤1, satisfy the following conditions: for each x,f(x,y) is an integrable function of y, and (∂f(x,y)/∂x) is a bounded function of (x,y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and dx d ∫ 0 1 f(x,y)dy=∫ 0 1 ∂x ∂ f(x,y)dy

Let f(x,y),0≤x,y≤1, satisfy the following conditions: for each x,f(x,y) is an integrable function of y, and (∂f(x,y)/∂x) is a bounded function of (x,y). Show that (∂f(x,y)/∂x) is a measurable function of y for each x and dx d ∫ 0 1 f(x,y)dy=∫ 0 1 ∂x ∂ f(x,y)dy