query: If a nonnegative continuous function is positive at a point, its integral is positive
positive_passages.docid: 30940
positive_passages.text: Prove the integral of $f$ is positive if $f ≥ 0$, $f$ continuous at $x_0$ and $f(x_0)>0$
negative_passages.docid: 154572
negative_passages.text: Continuity of a function at an isolated point
negative_passages.docid: 131992
negative_passages.text: A problem on continuous functions
negative_passages.docid: 120676
negative_passages.text: A certain element which makes functionals positive
negative_passages.docid: 12523
negative_passages.text: Supremum of a Continuous Function is Continuous
negative_passages.docid: 80643
negative_passages.text: Show that f(x) defined on [0,infinity) R to is continuous at 0.
negative_passages.docid: 86327
negative_passages.text: If the absolute value of a function is continuous, is the function continuous?
negative_passages.docid: 73807
negative_passages.text: Prove positive definiteness
negative_passages.docid: 64486
negative_passages.text: Show that for non-negative measurable functions $f,g$ with $fg \geq 1$ the inequality $(\int f^p)(\int g^p) \geq 1$ holds.
negative_passages.docid: 158180
negative_passages.text: An inequality of $\int_0^1 |f(x)|dx$
negative_passages.docid: 125910
negative_passages.text: Continuity of Integration for a measurable function
negative_passages.docid: 157485
negative_passages.text: Integral of limit of pointwise convergent sequence of non-negative measurable functions
negative_passages.docid: 70617
negative_passages.text: Continuity at a point of characteristic function iff the point is not boundary point
negative_passages.docid: 28619
negative_passages.text: Bound on integral implies bound on function
negative_passages.docid: 44607
negative_passages.text: Prove that a continuous function on a closed interval attains a maximum
negative_passages.docid: 58816
negative_passages.text: Existence of a continuous function which does not achieve a maximum.
negative_passages.docid: 143695
negative_passages.text: Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?