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39 Questions

If $f:\mathbb{R}\to\mathbb{R}$ is a left continuous function can the set of discontinuous points of $f$ have positive Lebesgue measure?

Does this Condition on Exit Times imply $X_t$ is a Local Supermartingale?

If every open set is a countable union of balls, is the space separable?

Considering Brownian bridge as conditioned Brownian motion

How to calculate the matrix exponential explicitly for a matrix which isn't diagonalizable?

Distribution of hitting time of line by Brownian motion

Is there a discrete-time analogue of Doléans-Dade exponential?

Lebesgue measure in $\mathbb{R}^2$ of uncountable union

If A is a subset of R with Lebesgue measure > 0 then are there a,b such that the measure of $[a,b]\cap A$ is b-a?

Convergence of Brownian integral

Can a collection of subsets of $\mathbb{N}$ such that no one set contains another be uncountable?

Is there a simpler proof of Van der Waerden's Theorem when there are only two colors?

Relationship between Hölder continuity and differentiability of Brownian motion

Limit of sums of iid random variables which are not square-integrable

Is $M^2-[M]$ a local martingale when $M$ is a local martingale?

What is the distribution of the position of the maximum of a Brownian bridge?

Example of a martingale which is not jointly measurable

Splitting a Poisson process according to time-dependent probabilities

How to show martingale is bounded in $L^1$?

Integral of alternating series

Are $L$-diffusions unique in law?

Showing equivalence of $\sigma$-algebras

How to show this random variable equals its conditional expectation?

An example of a projective sequence of measures on non-Borel spaces that does not extend to a probability on the product space?

Proving that a process is a Brownian motion

Characterizing previsible processes

Using Dominated Convergence Theorem

Little's Formula for M/G/1/c queue

Collecting coupons which arrive as a Poisson process

Galois group of successive quadratic extensions