query: Measure Theory and Probability Theory
positive_passages.docid: 23699
positive_passages.text: Reference book on measure theory
negative_passages.docid: 137203
negative_passages.text: Measurable cardinal existence condition
negative_passages.docid: 143214
negative_passages.text: Brownian motion - Hölder continuity
negative_passages.docid: 1474
negative_passages.text: How to prove limit of measurable functions is measurable
negative_passages.docid: 118353
negative_passages.text: For set of positive measure $E$, $\alpha \in (0, 1)$, there is interval $I$ such that $m(E \cap I) > \alpha \, m(I)$
negative_passages.docid: 52301
negative_passages.text: Omitting the hypotheses of finiteness of the measure in Egorov theorem
negative_passages.docid: 3023
negative_passages.text: Construction of a Borel set with positive but not full measure in each interval
negative_passages.docid: 60080
negative_passages.text: $E[e_te_s\Delta B_t\Delta B_s]$ for $\Delta B_t$ Brownian motion increments and $e_t(\omega)$ a measurable function.
negative_passages.docid: 62780
negative_passages.text: Another question on almost sure and convergence in probability
negative_passages.docid: 158494
negative_passages.text: Properties of special rectangle (measure)
negative_passages.docid: 99562
negative_passages.text: "Sum" of positive measure set contains an open interval?
negative_passages.docid: 19289
negative_passages.text: complement of a set and its measure
negative_passages.docid: 94945
negative_passages.text: Sum and product of Martingale processes
negative_passages.docid: 111915
negative_passages.text: Almost Sure Convergence and Bounded Expectation
negative_passages.docid: 84359
negative_passages.text: On Lebesgue Outer Measure of an interval
negative_passages.docid: 74355
negative_passages.text: Convergence in measure and almost everywhere
negative_passages.docid: 80
negative_passages.text: Convergence in measure implies convergence almost everywhere of a subsequence