I: 04, 52-53, LNM 39 (1967)
DELLACHERIE, Claude
Un complément au théorème de Weierstrass-Stone (
Functional analysis)
An easy but useful remark on the relation between the ``lattice'' and ``algebra'' forms of Stone's theorem, which apparently belongs to the folklore
Keywords: Stone-Weierstrass theoremNature: Original
Retrieve article from Numdam
II: 04, 43-74, LNM 51 (1968)
DOLÉANS-DADE, Catherine
Espaces $H^m$ sur les variétés, et applications aux équations aux dérivées partielles sur une variété compacte (
Functional analysis)
An attempt to teach to the members of the seminar the basic facts of the analytic theory of diffusion processes
Keywords: Sobolev spaces,
Second order elliptic equationsNature: Exposition Retrieve article from Numdam
III: 01, 1-23, LNM 88 (1969)
ARTZNER, Philippe
Extension du théorème de Sazonov-Minlos d'après L.~Schwartz (
Measure theory,
Functional analysis)
Exposition of three notes by L.~Schwartz (
CRAS 265, 1967 and
266, 1968) showing that some classes of maps between spaces $\ell^p$ and $\ell^q$ transform Gaussian cylindrical measures into Radon measures. The result turns out to be an extension of Minlos' theorem
Comment: Self-contained and detailed exposition, possibly still useful
Keywords: Radonifying mapsNature: Exposition Retrieve article from Numdam
VII: 19, 198-204, LNM 321 (1973)
MEYER, Paul-André
Limites médiales d'après Mokobodzki (
Measure theory,
Functional analysis)
Given a sequence of (classes of) random variables on a probability space which converges in some of the standard ways of measure theory, the problem is to find some universal method (independent from the underlying probability) to identify its limit. For convergence in probability, and thus for all strong $L^p$ topologies, Mokobodzki had discovered the procedure of rapid ultrafilters (see
304). The same problem is now solved for weak convergences, using a special kind of Banach limits
Comment: The paper contains a few annoying misprints, in particular p.199 line 9
s.c;s. should be deleted and line 17
atomique should be
absolument continu. For a misprint-free version see Dellacherie-Meyer,
Probabiliés et Potentiel, Volume C, Chapter X,
55--57
Keywords: Continuum axiom,
Weak convergence of r.v.'s,
Medial limitNature: Exposition Retrieve article from Numdam
XII: 01, 1-19, LNM 649 (1978)
PRATELLI, Maurizio
Une version probabiliste d'un théorème d'interpolation de G. Stampacchia (
Martingale theory,
Functional analysis)
This theorem is similar to the Marcinkievicz interpolation theorem, in the sense that at one endpoint a weak $L^p$ inequality is involved, but at the other endpoint the spaces involved are some $L^p$ and $BMO$. It concerns linear operators only, not sublinear ones like the Marcinkiewicz theorem. A closely related result, concerning the discrete-time case, had been proved earlier by Stroock,
Comm Pure Appl. Math.,
26, 1973
Keywords: Interpolation,
$BMO$Nature: Original Retrieve article from Numdam
XII: 12, 98-113, LNM 649 (1978)
DELLACHERIE, Claude;
MEYER, Paul-André;
YOR, Marc
Sur certaines propriétés des espaces de Banach $H^1$ et $BMO$ (
Martingale theory,
Functional analysis)
The general subject is the weak topology $\sigma(H^1,BMO)$ on the space $H^1$. Its relatively compact sets are characterized by a uniform integrability property of the maximal functions. A sequential completeness result (a Vitali-Hahn-Saks like theorem) is proved. Finally, a separate section is devoted to the denseness of $L^\infty$ in $BMO$, a subject which has greatly progressed since (the Garnett-Jones theorem, see
1519; see also
3021 and
3316)
Keywords: Hardy spaces,
$BMO$Nature: Original Retrieve article from Numdam
XIV: 25, 220-222, LNM 784 (1980)
YAN, Jia-An
Caractérisation d'ensembles convexes de $L^1$ ou $H^1$ (
Stochastic calculus,
Functional analysis)
This is a new and simpler approach to the crucial functional analytic lemma in
1354 (the proof that semimartingales are the stochastic integrators in $L^0$). That is, given a convex set $K\subset L^1$ containing $0$, find a condition for the existence of $Z>0$ in $L^\infty$ such that $\sup_{X\in K}E[ZX]<\infty$. A similar result is discussed for $H^1$ instead of $L^1$
Comment: This lemma, instead of the original one, has proved very useful in mathematical finance
Keywords: Semimartingales,
Stochastic integrals,
Convex functionsNature: Original Retrieve article from Numdam
XVI: 11, 153-158, LNM 920 (1982)
MEYER, Paul-André
Interpolation entre espaces d'Orlicz (
Functional analysis)
This is an exposition of Calderon's complex interpolation method, in the case of moderate Orlicz spaces, aiming at its application in
1609Keywords: Interpolation,
Orlicz spaces,
Moderate convex functionsNature: Exposition Retrieve article from Numdam
