query: $ L^{1}$ norm of a continuous non-zero function
positive_passages.docid: 72847
positive_passages.text: Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
negative_passages.docid: 9613
negative_passages.text: If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$
negative_passages.docid: 81240
negative_passages.text: Norm of an inverse operator: $\|T^{-1}\|=\|T\|^{-1}$?
negative_passages.docid: 143174
negative_passages.text: property of continuous function
negative_passages.docid: 87582
negative_passages.text: Some inequalities between 1- norm, 2- norm and infinity-norm: $\|x\|_2\leq\sqrt{\|x\|_1\| x\|_\infty}\leq\frac{1+\sqrt{n}}{2}\|x\|_2$
negative_passages.docid: 83494
negative_passages.text: Uniform continuity of $\ln(x)$
negative_passages.docid: 115417
negative_passages.text: Continuity of $L^1$ functions with respect to translation
negative_passages.docid: 5419
negative_passages.text: Continuous functions with $f^2(x)=g^2(x)\neq 0$
negative_passages.docid: 30036
negative_passages.text: Function in $H^1$, but not continuous
negative_passages.docid: 97158
negative_passages.text: Prove that the operator norm is a norm
negative_passages.docid: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
negative_passages.docid: 56958
negative_passages.text: bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
negative_passages.docid: 65876
negative_passages.text: A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
negative_passages.docid: 151410
negative_passages.text: Inequality of continuous functions
negative_passages.docid: 50730
negative_passages.text: Integral of bounded continuous function on $R$
negative_passages.docid: 132869
negative_passages.text: Show that any bounded linear functional on a normed linear space is continuous
negative_passages.docid: 51267
negative_passages.text: Showing a generalized version of the Hölder inequality for $L^{p}$ spaces