query: prove the continuity of $T_\phi f=\int_0^1 f(x)\phi(x) \,dx\\$
positive_passages.docid: 28289
positive_passages.text: Show that $Kf(x,y)=\int_0^1k(x,y) f(y) \,dy\\$ is linear and continuous
negative_passages.docid: 65889
negative_passages.text: Showing $\Phi(x)=\int_0^x (x-t)f(t)\,dt$ is twice differentiable and finding $\Phi''(x)$
negative_passages.docid: 23436
negative_passages.text: $f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
negative_passages.docid: 125910
negative_passages.text: Continuity of Integration for a measurable function
negative_passages.docid: 1626
negative_passages.text: How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
negative_passages.docid: 106531
negative_passages.text: A Fourier transform of a continuous $L^1$ function
negative_passages.docid: 145233
negative_passages.text: How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
negative_passages.docid: 61133
negative_passages.text: Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
negative_passages.docid: 151958
negative_passages.text: How to show $f'(0)$ exist and is equal to $1$?
negative_passages.docid: 67292
negative_passages.text: Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
negative_passages.docid: 5229
negative_passages.text: Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.
negative_passages.docid: 95429
negative_passages.text: If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
negative_passages.docid: 4062
negative_passages.text: prove that $f(x)=\log(1+x^2)$ is Uniform continuous with $\epsilon ,\delta$ ...
negative_passages.docid: 109570
negative_passages.text: How to show that the set of points of continuity is a $G_{\delta}$
negative_passages.docid: 98344
negative_passages.text: Prove that $\int_0^1[f''(x)]^2dx\ge4.$
negative_passages.docid: 34940
negative_passages.text: Continuity of $f(x) = x^n$
negative_passages.docid: 66504
negative_passages.text: Proof that $f$ is Lebesgue-integrable and calculate its integral